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

Give the vector from (2,7,0) to (1,3,5).
  • (3,4,5)
  • (1,4,5)
  • (3,10,5)
  • None of these
Find the vector which joins the point A(4,5,6) to B(10,11,12).
  • 14ˆi+16ˆj+18ˆk
  • 6ˆi6ˆj6ˆk
  • 6ˆi+6ˆj+6ˆk
  • None of these
Give the vector from (1,3,5) to (2,7,0).
  • (1,4,5)
  • (3,10,5)
  • (1,4,5)
  • None of these
Find the vector w with the initial point (4,1,2) and final point (1,6,5).
  • (3,5,3)
  • (0,7,3)
  • (3,5,3)
  • None of these
Find 2v, when u=(3,4,2) and v=(0,4,0).
  • (0,8,0)
  • (3,8,0)
  • (3,8,2)
  • None of these
Find the magnitude of the vector which joins the point A(4,5,6) to B(10,11,12).
  • 12.29
  • 10.39
  • 10.29
  • None of these
Which of the following is not a unit vector for all values of θ?
  • (cosθ)i(sinθ)j
  • (sinθ)i+(cosθ)j
  • (sin2θ)i(cosθ)j
  • (cos2θ)i(sin2θ)j
Find the vector w with the initial point (8,10,3) and final point (1,10,7).
  • (7,10,4)
  • (4,10,4)
  • (7,20,4)
  • None of these
The vector joining vector A to B  is represented by:
  • AB
  • BA
  • A+B
  • None of these
Find the magnitude of the vector which joins the point A(1,3,1) to B(0,0,0).
  • 21
  • 10
  • 11
  • None of these
Find the vector w with the initial point (a,b,c) and final point (a+1,b+2,c+3).
  • (a,b+2,c+3)
  • (a1,b2,c3)
  • (1,2,3)
  • None of these
Find the magnitude of the vector which joins the point A(a,2,c) to B(a+1,5,c+3).
  • 18
  • 21
  • 20
  • None of these
The coordinates of a point in 3-D space is (3,1,2). Then the position vector of the point is:
  • 3ˆi+3ˆj+3ˆk
  • 3ˆi+2ˆj+ˆk
  • 3ˆi+ˆj+2ˆk
  • ˆi+2ˆj+3ˆk
If a=(2,1,1),b=(1,1,0),c=(5,1,1) , then what is the unit vector parallel to a+bc in the opposite direction ?
  • ˆi+ˆj2ˆk3
  • ˆi2ˆj+2ˆk3
  • 2ˆiˆj+2ˆk3
  • None of the above.
The position vectors of the points A and B are respectively 3ˆi5ˆj+2ˆk and ˆi+ˆjˆk. What is the length of AB?
  • 11
  • 9
  • 7
  • 6
The unit vector perpendicular to the vector ˆiˆj and ˆi+ˆj forming a right handed system, is 
  • ˆk
  • ˆk
  • ˆiˆj2
  • ˆi+ˆj2
Point (4, 0) lies on ________.
  • \vec {XO}
  • \vec {YO}
  • \vec {OX}
  • \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.
  • True
  • False
If the points A and B are \left( 1,2,-1 \right) and  \left( 2,1,-1 \right) respectively, then  \vec { AB } is
  • \hat { i } +\hat { j }
  • \hat { i } -\hat { j }
  • 2\hat { i } +\hat { j } -\hat { k }
  • \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}=
  • \hat {i}
  • \hat {i} + j
  • \hat {k} - \hat {j}
  • \hat {i} + \hat {j} + \hat {k}
The Polygon Law of Vector Addition is simply an extension of ____________. 
  • Parallelogram Law of Vector Addition
  • Triangular Law of Vector Addition
  • Both A and B
  • None of the above
If \left| {\widehat a - \widehat b} \right| = \sqrt 3 , then  \left| {\widehat a + \widehat b} \right|  may be:-
  • 1
  • {{\sqrt 3 } \over 2}
  • Either (1) and (2)
  • 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| =
  • 10
  • \sqrt 10
  • 2\sqrt 10
  • 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 ________.
  • (2\sqrt {3}, -2\sqrt {3}, 2\sqrt {3})
  • \dfrac {3}{13} (4, 1, 3)
  • (1, -1, 1)
  • (2, -2, 2)
In Polygon Law of Vector Addition, the head of first vector is joined to the tail of last vector.
  • True
  • 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= _____________.
  • 2
  • 1
  • 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
  • \vec { a } +\vec { b }
  • \vec { a } \times \vec { b }
  • \vec { a } -\vec { b }
  • \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 ....
  • -\dfrac{15}{2}-10i
  • -\dfrac{15}{2}+10i
  • \dfrac{15}{2}+10i
  • \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
  • (0,4/3)
  • [0,2/3]
  • (11/9,4/3)
  • [0,1/3)
The vector
\vec a + \vec b,\vec a - k\vec b where k scalar are collinear, for
  • k=0
  • k=-1
  • k=1
  • 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 
  • \dfrac { 1 }{ 5 } \left( 5\hat { i } +\hat { j } -7\hat { k } \right)
  • \dfrac { 1 }{ 5 } \left( 5\hat { i } +9\hat { j } -13\hat { k } \right)
  • \left( \hat { i } -4\hat { j } +3\hat { k } \right)
  • \left( \hat { i } +4\hat { j } +3\hat { k } \right)
The position vector of point F, is?
  •  \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)
  • \vec{a}+\left|\dfrac{\vec{a}}{\vec{c}}\right|\vec{c}
  • \vec{a}+\dfrac{2|\vec{a}|}{|\vec{c}|}\vec{c}
  • \vec{a}-\left|\dfrac{\vec{a}}{\vec{c}}\right|\vec{c}
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}.
  • 3
  • -3
  • 33
  • -33
In a triangle ABC, if 2\vec { AC } =3\vec { CB }, then 2\vec { OA } +3\vec { OB } equals ?
  • 5\vec { OC }
  • -\vec { OC }
  • \vec { OC }
  • None of these
If |\overrightarrow{a}| = 5, |\overrightarrow{a} - \overrightarrow{b}|=8 and |\overrightarrow{a} + \overrightarrow{b}| = 10, then |\overrightarrow{b}| is equal to:
  • 1
  • \sqrt{57}
  • 3
  • 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 :
  • 1
  • \sqrt3
  • \dfrac {1}{2}
  • \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} ) =  
  • \dfrac {\pi}{3}
  • \dfrac {\pi}{4}
  • \dfrac {\pi}{6}
  • \dfrac {2 \pi}{3}
Which of the following expressions are meaningful?
  • \overrightarrow{u}.\left(\overrightarrow{v}\times \overrightarrow{w}\right)
  • \left(\overrightarrow{u}.\overrightarrow{v}\right).\overrightarrow{w}
  • \left(\overrightarrow{u}.\overrightarrow{v}\right)\overrightarrow{w}
  • \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
  • \overrightarrow{u}.\left(\overrightarrow{v}\times \overrightarrow{w}\right)
  • \left(\overrightarrow{v}\times \overrightarrow{w}\right).\overrightarrow{u}
  • \overrightarrow{v}.\left(\overrightarrow{u}\times \overrightarrow{w}\right)
  • \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 
  • 2 : 1
  • 4 : 3
  • 1 : 4
  • 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.
  • True
  • 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:
  • Along west
  • Along east
  • Zero
  • 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 
  • \frac{3}{2}(\bar{b}-\bar{a})
  • \frac{4}{3}(\bar{a}-\bar{b})
  • \frac{5}{6}(\bar{b}-\bar{a})
  • \frac{4}{3}(\bar{b}-\bar{a})
Two vector A and B have equal magnitudes. Then the vector A+B is perpendicular to 
  • A\times{B}
  • A-B
  • 3A-3B
  • 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
  • - 9 units
  • 9 units
  • -15 units
  • 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?
  • \vec{b}=0
  • \vec{b} \perp\vec{a}
  • \vec{b} is non-zero vector
  • \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 }
  • \vec { A } \times \vec { B }
  • \vec { 0 }
  • \vec{ C } \times \vec { B }
  • \vec { C } \times \vec { A }
\vec{r}  = \vec{x}\hat{i}+\vec{y}\hat{j} is the equation of:
  • yoz plane
  • a straight line joining the points \vec{i} and \vec{j}
  • zox plane
  • xoy plane
The unit vector in the direction of \overrightarrow{a} is 
  • \dfrac{\vec{a}}{|\vec{a}|}
  • \vec{a}|\vec{a}|
  • a^2
  • \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).
  • (9, -4)
  • (-9, -4)
  • (9, 4)
  • none of these
0:0:1


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