MCQ Questions for Class 12 Commerce Maths Vector Algebra Quiz 2

Give the vector from $$(2,-7,0)$$ to $$(1,-3,-5)$$.

0%
$$(3,4,-5)$$
0%
$$(-1,4,-5)$$
0%
$$(3,-10,-5)$$
0%
None of these

Find the vector which joins the point A$$(4,5,6)$$ to B$$(10,11,12)$$.

0%
$$14\hat i+16\hat j+18\hat k$$
0%
$$-6\hat i-6\hat j-6\hat k$$
0%
$$6\hat i+6\hat j+6\hat k$$
0%
None of these

Give the vector from $$(1,-3,-5)$$ to $$(2,-7,0)$$.

0%
$$(1,-4,5)$$
0%
$$(3,-10,-5)$$
0%
$$(1,4,5)$$
0%
None of these

Find the vector $$w$$ with the initial point $$(4,1,2)$$ and final point $$(1,6,5)$$.

0%
$$(3,-5,-3)$$
0%
$$(0,7,3)$$
0%
$$(-3,5,3)$$
0%
None of these

Find $$2v$$, when $$u=(3,4,-2)$$ and $$v=(0,-4,0)$$.

0%
$$(0,-8,0)$$
0%
$$(3,8,0)$$
0%
$$(3,-8,-2)$$
0%
None of these

Find the magnitude of the vector which joins the point $$A$$$$(4,5,6)$$ to $$B$$$$(10,11,12)$$.

0%
$$12.29$$
0%
$$10.39$$
0%
$$10.29$$
0%
None of these

Which of the following is not a unit vector for all values of $$\theta$$?

0%
$$(\cos\theta)i - (\sin\theta)j$$
0%
$$(\sin\theta)i + (\cos\theta)j$$
0%
$$(\sin2\theta)i - (\cos\theta)j$$
0%
$$(\cos2\theta)i - (\sin2\theta)j$$

Find the vector $$w$$ with the initial point $$(8,-10,3)$$ and final point $$(1,10,7)$$.

0%
$$(7,10,-4)$$
0%
$$(-4,10,4)$$
0%
$$(-7,20,4)$$
0%
None of these

The vector joining vector $$\vec{A}$$ to $$\vec{B}$$ is represented by:

0%
$$\vec{A}-\vec{B}$$
0%
$$\vec{B}-\vec{A}$$
0%
$$\vec{A}+\vec{B}$$
0%
None of these

Find the magnitude of the vector which joins the point $$A$$$$(-1,-3,-1)$$ to $$B$$$$(0,0,0)$$.

0%
$$\sqrt{21}$$
0%
$$\sqrt{10}$$
0%
$$\sqrt{11}$$
0%
None of these

Find the vector $$w$$ with the initial point $$(a,b,c)$$ and final point $$(a+1,b+2,c+3)$$.

0%
$$(a,b+2,c+3)$$
0%
$$(a-1,b-2,c-3)$$
0%
$$(1,2,3)$$
0%
None of these

Find the magnitude of the vector which joins the point $$A$$$$(a,2,c)$$ to $$B$$$$(a+1,5,c+3)$$.

0%
$$\sqrt{18}$$
0%
$$\sqrt{21}$$
0%
$$\sqrt{20}$$
0%
None of these

The coordinates of a point in $$3$$-D space is $$(3,1,2)$$. Then the position vector of the point is:

0%
$$3\hat i + 3\hat j + 3\hat k$$
0%
$$3\hat i + 2\hat j + \hat k$$
0%
$$3\hat i + \hat j + 2\hat k$$
0%
$$\hat i + 2\hat j + 3\hat k$$

If $$\vec{a} = (2, 1, -1), \vec{b} = (1,-1,0), \vec{c} = (5, -1, 1) $$ , then what is the unit vector parallel to $$ \vec{a} + \vec{b} - \vec{c} $$ in the opposite direction ?

0%
$$\dfrac{\hat{i}+\hat{j}-2 \hat{k}}{3}$$
0%
$$\dfrac{\hat{i}-2 \hat{j} + 2 \hat{k}}{3}$$
0%
$$\dfrac{2 \hat{i} - \hat{j} + 2 \hat{k}}{3}$$
0%
None of the above.

The position vectors of the points $$A$$ and $$B$$ are respectively $$3\hat { i } -5\hat { j } +2\hat { k } $$ and $$\hat { i } +\hat { j } -\hat { k } $$. What is the length of $$AB$$?

0%
$$11$$
0%
$$9$$
0%
$$7$$
0%
$$6$$

The unit vector perpendicular to the vector $$\hat{i}-\hat{j}$$ and $$\hat{i}+\hat{j}$$ forming a right handed system, is

0%
$$\hat{k}$$
0%
$$-\hat{k}$$
0%
$$\dfrac{\hat{i}-\hat{j}}{\sqrt{2}}$$
0%
$$\dfrac{\hat{i}+\hat{j}}{\sqrt{2}}$$

Point $$(4, 0)$$ lies on ________.

0%
$$\vec {XO}$$
0%
$$\vec {YO}$$
0%
$$\vec {OX}$$
0%
$$\vec {OY}$$

State the following statement is True or False

If the starting and end points of a vector are collinear, it is known as a unit vector.

0%
True
0%
False

If the points $$A$$ and $$B$$ are $$\left( 1,2,-1 \right)$$ and $$ \left( 2,1,-1 \right)$$ respectively, then $$ \vec { AB } $$ is

0%
$$\hat { i } +\hat { j } $$
0%
$$\hat { i } -\hat { j } $$
0%
$$2\hat { i } +\hat { j } -\hat { k } $$
0%
$$\hat { i } +\hat { j } +\hat { k } $$

If $$\vec {a} . \hat {i} = \vec {a} . (\hat {i} + \hat {j}) = \vec {a} (\hat {i} + \hat {j} + \hat {k})$$, thus $$\vec {a}=$$

0%
$$\hat {i}$$
0%
$$\hat {i} + j$$
0%
$$\hat {k} - \hat {j}$$
0%
$$\hat {i} + \hat {j} + \hat {k}$$

The Polygon Law of Vector Addition is simply an extension of ____________.

0%
Parallelogram Law of Vector Addition
0%
Triangular Law of Vector Addition
0%
Both A and B
0%
None of the above

If $$\left| {\widehat a - \widehat b} \right| = \sqrt 3 $$ , then $$\left| {\widehat a + \widehat b} \right|$$ may be:-

0%
$$1$$
0%
$${{\sqrt 3 } \over 2}$$
0%
Either (1) and (2)
0%
None of these

If $$\left| \overrightarrow { a } \right| =7,\ \left| \overrightarrow { b } \right| =11,\ \left| \overrightarrow { a } +\overrightarrow { b } \right| = 10\sqrt 3$$, then $$\left| \overrightarrow { a } -\overrightarrow { b } \right| =$$

0%
10
0%
$$\sqrt 10$$
0%
$$2\sqrt 10$$
0%
20

For $$A(1, -2, 4), B(5, -1, 7), C(3, 6, -2), D(4, 5, -1)$$, the projection of $$\overline {AB}$$ on $$\overline {CD}$$ is ________.

0%
$$(2\sqrt {3}, -2\sqrt {3}, 2\sqrt {3})$$
0%
$$\dfrac {3}{13} (4, 1, 3)$$
0%
$$(1, -1, 1)$$
0%
$$(2, -2, 2)$$

In Polygon Law of Vector Addition, the head of first vector is joined to the tail of last vector.

0%
True
0%
False

If $$\bar{a}$$ is unit vector, then $$|\bar{a}\times \hat{i}|^2+|\bar{a}\times \hat{j}|^2+|\bar{a}\times \hat{k}|^2=$$ _____________.

0%
$$2$$
0%
$$1$$
0%
$$0$$
0%
$$3$$

If $$\vec { a } $$ and $$\vec { b } $$ are non-zero non-collinear vectors, then $$\left[ \vec { a } \quad \vec { b } \quad \hat { i } \right] \hat { i } +\left[ \vec { a } \quad \vec { b } \quad \hat { j } \right] \hat { j } +\left[ \vec { a } \quad \vec { b } \quad \hat { k } \right] \hat { k } $$ is equal to

0%
$$\vec { a } +\vec { b } $$
0%
$$\vec { a } \times \vec { b } $$
0%
$$\vec { a } -\vec { b } $$
0%
$$\vec { b } \times \vec { a } $$

The vector $$z = 3 - 4i$$ is turned anticlockwise through an angle of $$180^{\circ}$$ and stretched $$\dfrac{5}{2}$$ times. The complex number corresponding to the newly obtained vector is ....

0%
$$-\dfrac{15}{2}-10i$$
0%
$$-\dfrac{15}{2}+10i$$
0%
$$\dfrac{15}{2}+10i$$
0%
$$\dfrac{15}{2}-10i$$

The set of values of $$c$$ for which the angle between the vectors $$cx\hat{i}-6\hat{j}+3\hat{k}$$ and $$x\hat{i}-2\hat{j}+2cx\hat{k}$$ is acute for every $$x\in R$$ is

0%
$$(0,4/3)$$
0%
$$[0,2/3]$$
0%
$$(11/9,4/3)$$
0%
$$[0,1/3)$$

The vector
$$\vec a + \vec b,\vec a - k\vec b$$ where $$k$$ scalar are collinear, for

0%
$$k=0$$
0%
$$k=-1$$
0%
$$k=1$$
0%
$$k=2$$

A line passes through the points whose position vectors $$ \hat { i } +\hat { j } -2\hat { k }$$ and $$\hat { i } -3\hat { j } +\hat { k }$$. Then the position vector of a point on it at a unit distance from the first point is

0%
$$\dfrac { 1 }{ 5 } \left( 5\hat { i } +\hat { j } -7\hat { k } \right)$$
0%
$$\dfrac { 1 }{ 5 } \left( 5\hat { i } +9\hat { j } -13\hat { k } \right)$$
0%
$$\left( \hat { i } -4\hat { j } +3\hat { k } \right)$$
0%
$$\left( \hat { i } +4\hat { j } +3\hat { k } \right)$$

The position vector of point F, is?

0%
$$\dfrac{{3\left| {\overline a } \right|\,\left| {\overline c } \right|}}{{3\left| {\overline c } \right| + 2\left| {\overline a } \right|}}\,\,\,\left( {\dfrac{{\overrightarrow a }}{{\left| {\overline a } \right|}} + \dfrac{{\overrightarrow c }}{{\left| {\overline c } \right|}}} \right)$$
0%
$$\vec{a}+\left|\dfrac{\vec{a}}{\vec{c}}\right|\vec{c}$$
0%
$$\vec{a}+\dfrac{2|\vec{a}|}{|\vec{c}|}\vec{c}$$
0%
$$\vec{a}-\left|\dfrac{\vec{a}}{\vec{c}}\right|\vec{c}$$

Explanation

According to question:

$$\begin{array}{l} B=\overrightarrow { a } +\overrightarrow { c } \\ \overrightarrow { E } =\dfrac { { 2\overrightarrow { c } +\overrightarrow { a } +\overrightarrow { c } } }{ 3 } =\dfrac { { 3\overrightarrow { c } +\overrightarrow { a } } }{ 3 } \\ then, \\ Position\, vector\, is: \\ \, \, \, \, \, \overrightarrow { OP } =\lambda \, (\overrightarrow { a } +\overrightarrow { c } )-----(i) \\ \, \, \, \, Now, \\ \, \, \, \, \, \, \, positon\, \, vector\, of\overrightarrow { \, p } : \\ \, \, \, \, \, \overrightarrow { p } =\overrightarrow { a } +\mu \left( { \dfrac { { 3\overrightarrow { c } +\overrightarrow { a } } }{ 3 } -\overrightarrow { a } } \right) \\ \, \, \, \overrightarrow { p } =\overrightarrow { a } +\mu \left( { \dfrac { { 3\overrightarrow { c } -2\overrightarrow { a } } }{ 3 } } \right) -----(ii) \\ Now,\, equating\, \, eqn.\, \, (i)\, \, \& \, (ii) \\ \lambda \, \left( { \dfrac { { \overrightarrow { a } } }{ { \left| { \overline { a } } \right| } } +\dfrac { { \overrightarrow { c } } }{ { \left| { \overline { c } } \right| } } } \right) =\overrightarrow { a } +\dfrac { \mu }{ 3 } \left( { 3\overrightarrow { c } -2\overrightarrow { a } } \right) \\ \dfrac { \lambda }{ { \left| { \overline { a } } \right| } } =1-\dfrac { { 2\mu } }{ 3 } \, \, \, \, \, \, \, (cofficient\, compare) \\ \dfrac { \lambda }{ { \left| { \overline { a } } \right| } } =\dfrac { { 3\mu } }{ 3 } ,\, \, \, \, \, \, \, \, \, \mu =\dfrac { \lambda }{ { \left| { \overline { a } } \right| } } \\ And, \\ \dfrac { \lambda }{ { \left| { \overline { a } } \right| } } =1-\dfrac { 2 }{ 3 } .\, \dfrac { \lambda }{ { \left| { \overline { c } } \right| } } \\ \lambda \left( { \dfrac { 1 }{ { \left| { \overline { a } } \right| } } +\dfrac { 2 }{ 3 } .\, \dfrac { 1 }{ { \left| { \overline { c } } \right| } } } \right) =1 \\ \lambda =\dfrac { { 3\left| { \overline { a } } \right| \, \left| { \overline { c } } \right| } }{ { 3\left| { \overline { c } } \right| +2\left| { \overline { a } } \right| } } \\ \, positon\, \, vector\, of\overrightarrow { \, p } : \\ \overrightarrow { p } =\dfrac { { 3\left| { \overline { a } } \right| \, \left| { \overline { c } } \right| } }{ { 3\left| { \overline { c } } \right| +2\left| { \overline { a } } \right| } } \, \, \, \left( { \dfrac { { \overrightarrow { a } } }{ { \left| { \overline { a } } \right| } } +\dfrac { { \overrightarrow { c } } }{ { \left| { \overline { c } } \right| } } } \right) \\ so\, ,\, the\, correct\, \, option\, is\, A. \end{array}$$

If $$\bar{a}=2\bar{i}+\bar{j}+\bar{k}, \bar{b}=\bar{i}+5\bar{j}, \bar{c}=4\bar{i}+4\bar{j}-2\bar{k}$$ then the length of the projection of $$(3\bar{a}-2\bar{b})$$ in the direction of $$\bar{c}$$.

0%
$$3$$
0%
$$-3$$
0%
$$33$$
0%
$$-33$$

In a triangle ABC, if $$ 2\vec { AC } =3\vec { CB }$$, then $$2\vec { OA } +3\vec { OB }$$ equals ?

0%
$$5\vec { OC }$$
0%
$$-\vec { OC }$$
0%
$$\vec { OC }$$
0%
None of these

If $$|\overrightarrow{a}| = 5, |\overrightarrow{a} - \overrightarrow{b}|=8$$ and $$|\overrightarrow{a} + \overrightarrow{b}| = 10$$, then $$|\overrightarrow{b}|$$ is equal to:

0%
$$1$$
0%
$$\sqrt{57}$$
0%
$$3$$
0%
$$57$$

If the vector $$OP$$ in $$XY$$ plane whose magnitude is $$\sqrt3$$ makes an angle $$60^o$$ with $$Y-$$ axis, the length of the component of the vector in direction of $$X-$$ axis is :

0%
$$1$$
0%
$$\sqrt3$$
0%
$$\dfrac {1}{2}$$
0%
$$\dfrac {3}{2}$$

If $$ | \overline{a} | = 1 , | \overline{b} | = 2, | \overline{a} - \overline{b} |^2 + | \overline{a} + 2 \overline{b} |^2 = 20, $$ then $$ ( \overline{a} , \overline{b} ) = $$

0%
$$ \dfrac {\pi}{3} $$
0%
$$ \dfrac {\pi}{4} $$
0%
$$ \dfrac {\pi}{6} $$
0%
$$ \dfrac {2 \pi}{3} $$

Which of the following expressions are meaningful?

0%
$$\overrightarrow{u}.\left(\overrightarrow{v}\times \overrightarrow{w}\right) $$
0%
$$\left(\overrightarrow{u}.\overrightarrow{v}\right).\overrightarrow{w}$$
0%
$$\left(\overrightarrow{u}.\overrightarrow{v}\right)\overrightarrow{w} $$
0%
$$\overrightarrow{u}\times \left(\overrightarrow{v}.\overrightarrow{w}\right)$$

For three vectors $$\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$$ which of the following expressions is not equal to any of remaining is

0%
$$\overrightarrow{u}.\left(\overrightarrow{v}\times \overrightarrow{w}\right)$$
0%
$$\left(\overrightarrow{v}\times \overrightarrow{w}\right).\overrightarrow{u} $$
0%
$$\overrightarrow{v}.\left(\overrightarrow{u}\times \overrightarrow{w}\right)$$
0%
$$\left(\overrightarrow{u}\times \overrightarrow{v}\right).\overrightarrow{w}$$

The ratio in which the line joining $$(2,-4,3)$$ and $$(-4,5,-6)$$ is divided by the plane $$3x+2y+z-4=0$$ is

0%
$$2 : 1$$
0%
$$4 : 3$$
0%
$$1 : 4$$
0%
$$ 2 : 3$$

State true or false.

The vectors $$\vec { a } = - 4 \hat { i } - \hat { j } , \vec { b } = \hat { i } - 4 \hat { j } \text { and } \vec { c } = 3 \hat { i } + 5 \hat { j }$$ form a right angled-triangle.

0%
True
0%
False

A vector $$\overrightarrow { A } $$ points vertically downward(south)and $$\overrightarrow { B } $$ points towards east, then the vector product $$\overrightarrow { A } \times \overrightarrow { B } $$ is:

0%
Along west
0%
Along east
0%
Zero
0%
Outwards or inwards

$$\bar{a}$$ and $$\bar{b}$$ are the position vectors of A and B respectively. Points P and Q divide AB, internally and externally in the same ratio 2:1 , then PQ is equal to

0%
$$\frac{3}{2}(\bar{b}-\bar{a})$$
0%
$$\frac{4}{3}(\bar{a}-\bar{b})$$
0%
$$\frac{5}{6}(\bar{b}-\bar{a})$$
0%
$$\frac{4}{3}(\bar{b}-\bar{a})$$

Two vector $$A$$ and $$B$$ have equal magnitudes. Then the vector $$A+B$$ is perpendicular to

0%
$$A\times{B}$$
0%
$$A-B$$
0%
$$3A-3B$$
0%
All of these

The work done by the force $$\vec { F } = 2 \hat { i } - \hat { j } - \hat { \mathbf { k } }$$ in moung an object along the vector $$3 \hat { i } + 2 j - 5 \hat { k }$$ is

0%
$$- 9$$ units
0%
$$9$$ units
0%
$$-15$$ units
0%
None of these

Let $$\vec{a}=\hat{i}+\hat{j}+\hat{k}$$ and $$\vec{b}$$ is a vector such that $$\vec{a}.\vec{b}=0$$ and $$\vec{a}\times \vec{b}=0$$. Then which of following is correct?

0%
$$\vec{b}=0$$
0%
$$\vec{b} \perp\vec{a}$$
0%
$$\vec{b}$$ is non-zero vector
0%
$$\vec{b}$$ is parallel to $$\vec{a}$$

Given that $$\vec{ A } \times \vec{ B } =\vec{ B } \times \vec { C } =\vec { 0 } $$ if $$\vec{ A } \vec { B } \vec { C } $$ are not null vectors, Find the value of $$\vec{ A } \times \vec{ C } $$

0%
$$\vec { A } \times \vec { B } $$
0%
$$\vec { 0 } $$
0%
$$\vec{ C } \times \vec { B } $$
0%
$$\vec { C } \times \vec { A } $$

$$\vec{r} = \vec{x}\hat{i}+\vec{y}\hat{j}$$ is the equation of:

0%
$$yoz$$ plane
0%
a straight line joining the points $$\vec{i}$$ and $$\vec{j}$$
0%
$$zox$$ plane
0%
$$xoy$$ plane

The unit vector in the direction of $$\overrightarrow{a}$$ is

0%
$$\dfrac{\vec{a}}{|\vec{a}|}$$
0%
$$\vec{a}|\vec{a}|$$
0%
$$a^2$$
0%
$$\hat{i}$$

If $$\vec{a}$$ be the position vector whose tip is (5,-3), find the coordinates of a point B such that $$ \vec{AB} = \vec{a},$$ the coordinates of A being (4,-1).

0%
(9, -4)
0%
(-9, -4)
0%
(9, 4)
0%
none of these

CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 2 - MCQExams.com

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Practice Class 12 Commerce Maths Quiz Questions and Answers

CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 2 - MCQExams.com

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Practice Class 12 Commerce Maths Quiz Questions and Answers

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