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CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 1 - MCQExams.com

If |C|2=60 and C×(ˆi+2ˆj+5ˆk)=0, then a value of C(7ˆi+2ˆj+3ˆk) is :
  • 42
  • 24
  • 122
  • 12
In a parallelogram ABCD, |AB|=a,|AD|=b and |AC|=c, then DB.AB has the value
  • 12(a2+b2+c2)
  • 14(a2+b2c2)
  • 13(b2+c2a2)
  • 12(a2+b2c2)
Let P, Q, R and S be the points on the plane with position vectors 2ˆiˆj, 4ˆi, 3ˆi+3ˆj and 3ˆi+2ˆj respectively. The quadrilateral PQRS must be a
  • parallelogram, which is neither a rhombus nor a rectangle
  • square
  • rectangle, but not a square
  • rhombus, but not a square
  • Statement -1 is True, Statement -2 is True; Statement-2 is a correct explanation for Statement-1
  • Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1
  • Statement -1 is True, Statement -2 is False
  • Statement -1 is False, Statement -2 is True
ABCD is a parallelogram and AC,BD be its diagonals Then AC+BD is
  • 2AB
  • 2BC
  • 3AB
  • 3BC
The triangle ABC is defined by the vertices A=(0,7,10) , B=(1,6,6) and C=(4,9,6). Let D be the foot of the attitude from B to the side AC then BD is
  • ¯i+2¯j+2¯k
  • ¯i+2¯j+2¯k
  • ¯i+2¯j2¯k
  • ¯i2¯j+2¯k
The point C=(125,15,45) divides the line segment AB in the ratio 3:2. If B=(2,1,2) then A is
  • (3,1,1)
  • (3,1,1)
  • (3,1,1)
  • (3,1,1)
Let A=ˆi+6i+6k,B=4ˆi+9ˆi+6ˆk,G=53ˆi+223ˆj+223ˆk. If G is the centroid then the triangle ABC is
  • A right angled triangle
  • A right angled isosceles triangle
  • An isosceles triangle
  • An equilateral triangle
If A(¯a) , B(¯b) and C(¯c) be the vertices of a triangle ABC whose circumcentre is the origin then orthocentre is given by
  • ¯a+¯b+¯c
  • ¯a+¯b+¯c3
  • ¯a+¯b+¯c2
  • ¯a+¯b+¯c4
Let a,b,c,d be the position vectors of the points A,B,C,D respectively. The condition for the figure ABCD to be a parallelogram is
  • ˆa+ˆb=ˆc+ˆd
  • ˆa+ˆb=ˆc+ˆd=0
  • ˆa+ˆc=ˆb+ˆd
  • ˆa+ˆc=ˆb+ˆd=0
Let 2ˆi+ˆk=a, 3ˆj+4ˆk=b, 8ˆi3ˆj =c. If a=xb+yc, then (x,y) is equal to
  • (12,12)
  • (13,13)
  • (14,14)
  • (34,34)
If G is the centroid of the triangle ABC then GA+GB+GC is equal to 
  • AB
  • BC
  • 4GA
  • 0
If the position vectors of the points A,B,C,D are(0,2,1), (3,1,1), (5,3,2),(2,4,1) respectively and if PA+PB+PC+PD=0 then the position vector of P is
  • (0,52,54)
  • (52,52,54)
  • (52,0,54)
  • (52,54,0)
Let ABC be a triangle and let S be its circumcentre and O be its orthocentre. The ¯SA+¯SB+¯SC=
  • 4¯SO
  • 3¯SO
  • 2¯SO
  • ¯SO
If a×b=b×a, then
  • ab
  • a=kb
  • This result is impossible
  • This result is always true.
Taking O' as origin and the position vectors of A,B are i+3j2k,3i+j2k. The vector OC is bisecting the angle AOB and if C is a point on line AB then C is
  • 4(i+jk)
  • 2(i+jk)
  • (i+jk)
  • 6(i+jk)
The resultant of two concurrent forces nOP and mOQ is (m+n)OR. Then R divides PQ in the ratio
  • m:n
  • n:m
  • 1:n
  • m:1
P,Q,R,S have position vectors ¯p,¯q,¯r,¯s respectively such that ¯p¯q=2(¯s¯r), then which of the following is correct
  • PQ and RS bisect each other
  • PQ and PR bisect each other
  • PQ and RS trisect each other
  • QS and PR trisect each other
Let A=ˆi+2ˆj+3ˆk, B=4ˆi+2ˆj, C=2ˆi+2ˆj+2ˆk. Then the ratio in which C divides AB is
  • 3:4
  • 1:3
  • 1:2
  • 1:1
If ¯p is the position vector of the orthocentre and ¯g is the position vector of the centroid of the triangle ABC when circumcenter is the origin and if ¯p=λ¯g then λ=
  • 3
  • 2
  • 13
  • 23
Let A=(3,4,8) and B=(5,6,4), then the coordinates of the point in which the XY- plane or XOY plane divides the line segment AB is
  • (7,8,0)
  • (73,83,0)
  • (72,82,0)
  • (0,73,83)
If 3a+4b7c=0 then the ratio in which C(c) divides the join of A(a) and B(b) is
  • 1:2
  • 2:3
  • 3:2
  • 4:3
If a+2b,2a+b be the position vectors of the points A and B, then the position vector of the point C which divides AB internally in the ratio 2:1 is
  • 5a4b3
  • 5a+4b3
  • 5a2b3
  • 5a+2b3
In ΔABC, P, Q, R are points on BC, CA, AB respectively, dividing them in the ratio 1:4, 3:2 and 3:7. The point S divides AB in the ratio 1:3. Then |¯AP+¯BQ+¯CR||¯CS| is
  • 15
  • 25
  • 52
  • 710
If \vec a=\hat i+2\hat j and \vec b = 3\hat j, then \vec a\cdot\vec b=
  • 3
  • -3
  • 6
  • -6
If \overline{a} and \overline{b} are position vectors of A and B respectively, then the position vector of a point C in AB produced such that \overline{AC}=3\overline{AB} is
  • 3\overline{a}-\overline{b}
  • 3\overline{b}-\overline{a}
  • 3\overline{a}-2\overline{b}
  • 3\overline{b}-2\overline{a}
The projection of \displaystyle a=3i-j+5k on \displaystyle b=2i+3j+k is
  • \displaystyle 8/\sqrt{\left ( 35 \right )}
  • \displaystyle 8/\sqrt{\left ( 39 \right )}
  • \displaystyle 8/\sqrt{\left ( 14 \right )}
  • \displaystyle \sqrt{\left ( 14 \right )}
For O being the origin and 3 points P,Q and R lie on a plane. If \displaystyle \vec{PO}+\vec{OQ}=\vec{QO}+\vec{OR}, then P, Q, R are
  • the vertices of an equilateral triangle
  • the vertices of an isoceles triangle
  • collinear
  • none of these
If \left[ \overrightarrow { a } \overrightarrow { b } \overrightarrow { c }  \right] =1 then \frac { \overrightarrow { a } .\overrightarrow { b }\times \overrightarrow { c }  }{ \overrightarrow { c }\times \overrightarrow { a } .\overrightarrow { b }  } +\frac { \overrightarrow { b } .\overrightarrow { c }\times \overrightarrow { a }  }{ \overrightarrow { a }\times \overrightarrow { b } .\overrightarrow { c }  } +\frac { \overrightarrow { c } .\overrightarrow { a }\times \overrightarrow { b }  }{ \overrightarrow { b }\times \overrightarrow { c } .\overrightarrow { a }  } is equal to
  • 3
  • 1
  • -1
  • None of these
The projection \displaystyle 2\hat{i}+3\hat{j}-2\hat{k} on the vector \displaystyle \hat{i}+2\hat{j}-3\hat{k} is
  • \displaystyle \frac{1}{\sqrt{14}}
  • \displaystyle \sqrt{14}
  • \displaystyle \frac{2}{\sqrt{14}}
  • none of these
Let \vec{AB}= 3\widehat {i} + \widehat{j}- \widehat{k} and \vec{AC}=\widehat{i} -\widehat{j} +3\widehat{k} and a point P on the line segment BC is equidistant from AB and AC, then \vec{AP} is 
  • 2\widehat{i}- \widehat{k}
  • \widehat{i}- 2\widehat{k}
  • 2\widehat{i} + \widehat{k}
  • None of these
The vector sum of (N) coplanar forces, each of magnitude F, when each force is making an angle of
\frac{2\pi }{N} with that preceding one, is :
  • F
  • \frac{NF}{2}
  • NF
  • Zero
If \vec{a}=3\hat{i}-2\hat{j}+\hat{k},\vec{b}=2\hat{i}-4\hat{j}-3\hat{k}\vec{c}=-1\hat{i}+2\hat{j}+2\hat{k} then \vec{a}+\vec{b}+\vec{c}=
  • 3\hat{i}-4\hat{j} 
  • 3\hat{i}+4\hat{j} 
  • 4\hat{i}-4\hat{j} 
  • 4\hat{i}+4\hat{j} 
Four point charges {q}_A=2\mu C{q}_B=5\mu C{q}_C=2\mu C{q}_D=5\mu C are located at the four corners of a square ABCD of side 10 cm. The force on a charge of 1\mu C placed at the centre of the square is
  • Zero
  • Towards AB
  • Towards BC
  • Towards AD
Namita walks 14 metres towards west, then turns to her right and walks 14 metres and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and the present position ?
  • 10
  • 24
  • 28
  • 38
If O is origin and C is the mid point of A(2, -1) and B(-4,3). Then value of OC is
  • i + j
  • -i + j
  • i - j
  • -i - j
A vector whose initial and terminal points coincide, is 
  • Zero Vector
  • Equal Vectors
  • Null Vector
  • Unit Vector
If \vec{a}, \vec{b}, \vec{c} are three non coplanar vectors, then (\vec{a}+\vec{b}+\vec{c})[(\vec{a}+\vec{b}) \times (\vec{a}+\vec{c})] is :
  • 0
  • 2 [\vec{a}. \vec{b}. \vec{c}]
  • - [\vec{a}. \vec{b}. \vec{c}]
  • [\vec{a}. \vec{b}. \vec{c}]
ABCDEF is a regular hexagon . Let \displaystyle \vec { AB } =a and \displaystyle \vec { BC } =b. Express the vectors \displaystyle \vec { AC } in terms if a and b.
426332.PNG
  • \vec{a}+\vec{b}
  • \vec{a}-\vec{b}
  • 2\vec{a}
  • None of these
Given that u is a vector of length 2, v is a vector of length 3 and the angle between them when placed tail to tail is \displaystyle 45^{\circ} , which option is closest to the exact value of \vec u\cdot\vec v ?
  • 4.5
  • 6.2
  • 4.2
  • 5.1
Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true?
426348.PNG
  • b+e=f
  • b+c=f
  • d+c=f
  • d+e=f
Given the points A(-2,3,4),B(3,2,5),C(1,-1,2),\,\&\,D(3,2,-4) The projection of the vector \displaystyle \underset{AB}{\rightarrow} on the vector \displaystyle \underset{CD}{\rightarrow} is
  • \displaystyle \frac{22}{3}
  • \displaystyle -\frac{21}{4}
  • \displaystyle \frac{1}{7}
  • -47
A zero vector has
  • Any direction
  • Many directions
  • No direction
  • None of these
If 2\vec{a}+3\vec{b}-5\vec{c}=\vec{0}, then ratio in which \vec{c} divides \vec{AB} is
  • 3:2 internally
  • 3:2 externally
  • 2:3 internally
  • 2:3 externally
Let ABCD be a parallelogram whose diagonals intersect at P and O be the origin, then \vec { OA } +\vec { OB } +\vec { OC } +\vec { OD } equals
  • \vec { OP }
  • 2\vec { OP }
  • 3\vec { OP }
  • 4\vec { OP }
The system of vectors i, j, k is
  • Orthogonal
  • Collinear
  • Coplanar
  • None of these
The projection of \displaystyle \overset { \rightarrow  }{ a } =2\overset { \wedge  }{ i } +3\overset { \wedge  }{ j } -2\overset { \wedge  }{ k }  on \displaystyle \overset { \rightarrow  }{ b } =\overset { \wedge  }{ i } +2\overset { \wedge  }{ j } +3\overset { \wedge  }{ k }  is:
  • \displaystyle \frac { 1 }{ \sqrt { 14 } }
  • \displaystyle \frac { 2 }{ \sqrt { 14 } }
  • \displaystyle \frac{-1}{ \sqrt { 14 } }
  • \displaystyle \frac { -2 }{ \sqrt { 14 } }
If \vec {a} is a nonzero vector of magnitude 'a' and \lambda a nonzero scalar, then \lambda{\vec {a}} is unit vector if
  • \lambda=1
  • \lambda=-1
  • a=|\lambda|
  • a=\dfrac {1}{|\lambda|}
Find u+v, when u=(3,4,-2) and v=(0,-4,0).
  • (3,-8,-2)
  • (-3,0,2)
  • (3,0,-2)
  • None of these
Find the vector w with the initial point (9,4) and final point (12,6).
  • (21,10)
  • (3,2)
  • (-21,2)
  • none of these
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers