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CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 13 - MCQExams.com

If  u=ab ;v=a+b  & |a|=|b|=2, then |u×υ| is equal to:
  • 2(4(a.b)2)
  • 2(16+(a.b)2)
  • 2(4(a.b)2)
  • 2(16(a.b)2)
r.ˆi=2r.ˆj=4r.ˆk and |r|=84, then |r.(2ˆi3ˆj+ˆk)| is equal to 
  • 0
  • 2
  • 4
  • 6
If ˉa=ˆi+ˆj2ˆk,ˉb=2ˆi0ˆj+ˆk,ˉc=3ˆiˆk and ˉc=mˉa+nˉb then m + n = ....
  • 0
  • 1
  • 2
  • -1
If the position vectors of A,B,C,D are 3ˆi+2ˆj+ˆk,4ˆi+5ˆj+5ˆk,4ˆi+2ˆj2ˆk,6ˆi+5ˆjˆk respectively then the position vector of the point of intersection of ¯AB and ¯CD is
  • 2ˆi+ˆj3ˆk
  • 2ˆiˆj+3ˆk
  • 2ˆi+ˆj+3ˆk
  • 2ˆiˆj3ˆk
Let a=ˆiˆj,b=ˆiˆj=c=ˆiˆj, if d is a unit vector such that a.d=0=|bcd| then d equals:
  • ±ˆi+ˆj2ˆk6
  • ±ˆi+ˆj2ˆk3
  • ±ˆi+ˆj+2ˆk3
  • ±ˆk
If a=ij,b=i+j,c=i+3j+5k and n is a unit vector such that b,n=0,a,n=0 then the value of |c,n| is equal to
  • 1
  • 3
  • 5
  • 2
The value of |a׈i|2+|a׈j|2+|a׈k|2 is 
  • a2
  • 2a2
  • 3a2
  • none of these
The values of λ such that (x,y,z)(0,0,0) and (ˆi+ˆj+3ˆk)x+(3ˆi3ˆj+ˆk)y+(4ˆi+5ˆj)z=λ(xˆi+yˆj+zˆk) are
  • 0,1
  • 0,1
  • 1,1
  • 0,1,1
Let u, v, w be such that |u| = 1, |v| = 2, |w| = 3 . If the projection v along u is equal to that of w along u and v, w are perpendicular to each other , then |uv+w| equals 
  • 14
  • 7
  • 2
  • 14
Vector x satisfying the relation A.¯x=c and A×x=B is
  • cA(¯A×B)|A|
  • cA(A×B)|A|2
  • cA+(A×B)|A|2
  • None
For any vector a, the value of (a׈i)2+(a׈j)2+(a׈k)2 is equal to
  • 4|a|2
  • 2|a|2
  • |a|2
  • 3|a|2
let ˉa be a unit vector and ˉb be a non-zero vector not parallel to ˉa if two sides of a triangle are represented by the vectors 3(ˉa×ˉb)andˉb(ˉa.ˉb)ˉa then the angles of triangle are 
  • 90,60,30
  • 45,45,90
  • 60,60,60
  • 75,45,60
In a triangle ABC, if A=(0,0),B=(3,33),C=(33,3) then the vector of magnitude 22 units directed along ¯AO, where O is the circumcentre of triangle ABC is?
  • (13)ˉi+(1+3)ˉj
  • 3ˉi+2ˉj
  • ˉi3ˉj
  • ˉi+2ˉj
In a parallelogram ABD, |_AB|=a,|_AD|=b and |_AC|=c,, _AB._DB has the value :
  • 12(3a2+b2c2)
  • 12(a2b2+c2)
  • 12(a2+b2c2)
  • 13(b2+c2a2)
If the position vectors of the vertices A,B and C of a ΔABC are respectively 4ˆi+7ˆj+8ˆk,2ˆi+3ˆj+4ˆk and 2ˆi+5ˆj+7ˆk, then the position vector of the point, where the bisector of A meets BC is:
  • 12(4ˆi+8ˆj+11ˆk)
  • 13(6ˆi+13ˆj+18ˆk)
  • 14(8ˆi+14ˆj+19ˆk)
  • 13(6ˆi+8ˆj+15ˆk)
If|a| =2 and |b|=3 and |a|.|b| =Then (a x (a x (a x (a x b)))) is equal to 
  • 4ˆb
  • 4ˆb
  • 4ˆa
  • 4ˆa
If C is the mid-point of AB and P is any point outside AB , then
  • PA + PB + PC = 0
  • PA + PB + 2PC = 0
  • PA PB = PC
  • PA PB = 2PC
If a and b are vectors such that |a+b|=29 and a×(2i+3j+4k)=(2i+3j+4k)×b, then a possible value of (a+b)(7i+2j+3k) is 
  • 0
  • 3
  • 4
  • 8
If ˆu and ˆv are unit vectors and θ is the acute angle between them , then 2ˆu 3ˆv is a unit vector for
  • No value of θ
  • Exactly one value of θ
  • Exactly two values of θ
  • More than two values of θ
Let aˆi  ˆj, bˆj  ˆk, cˆk  ˆi. If d is a unit vector such that a.d = 0 = |bcd| then d equals :
  • ˆi+ˆj2ˆk6
  • ˆi+ˆjˆk3
  • ˆi+ˆj+ˆk3
  • ˆk
The value of λ for (x,y,z)(0,0,0) and (i+j+3k)x+(3i3j+k)y+(4i+5j)z=λ(xi+yj+zk) are
  • 0, -1
  • 0, 1
  • -2, 0
  • 0, 2
If a,b,c are unit vectors such that a+b+c=0 then the value of a.b+b.c+c.a. is 
  • 1
  • -1
  • -3/2
  • none of these
If ¯a=2¯i+3¯j+4¯k and ¯b=2¯i2¯j+3¯k then ¯a.¯b is 
  • 2
  • -2
  • 6
  • none of these
Let position vector of the orthocentre of ABC be r. then, which of the following statement(s) is\are correct (Given position vector of points aˆi,bˆj,cˆk and abc=0)

  • r.ˉi=a1a2+1b2+1c2
  • r.ˉi=1a(1a2+1b2+1c2)
  • r.ˉir.ˉj+r.ˉjr.ˉk+r.ˉkr.ˉi=ab+bc+ca
  • r.ˉir.ˉj+r.ˉjr.ˉk+r.ˉkr.ˉi=ba+cb+ac
If C is the mid point of AB and P is any point outside AB , then
  • PA + PB + PC = 0
  • PA + PB + 2PC = 0
  • PA + PB = PC
  • PA + PB = 2PC
A particle in a plane from A to E along the shown path. It is given that AB=BC=DE=10 metre. Then the magnitude of net displacement of particle is :
1337385_0185cb4e36554daba9ee1f911656980b.PNG
  • 10 m
  • 15 m
  • 5 m
  • 20 m
Let a=i<j(1nCi+1nCj) and b=i<j(inCi+jnCj), then?
  • b=(n1)a
  • b=(n+1)a
  • b=n2a
  • b=na
In parallelogram ABCD, |¯AB|=a,|¯AD|=b and |¯AC|=c then ¯DB,¯AB has the value
  • 3a2+b2c22
  • 3b2+c2a22
  • 3c2+b2a22
  • a2+b2+c22
If ni=1ai=0 where |ai|=1i, then the value of 1i<jnaiaj is
  • n/2
  • n
  • n/2
  • n
If the vectors abc satisfying a + b + 2c = 0 . If |a| = 1 , |b| = 4 , |c| = 2 , then a.b + b.c + c.a
  • 72
  • 172
  • 172
  • 72
The projection of the join of the point (3, 4, 2), (5, 1, 8) on the line whose d.c.'s are (27,37,67) is 
  • 7
  • (4613)
  • (4213)
  • (3813)
If a,b and care three mutually perpendicular vectors, then the projection of the vector |a|a|+mb|b|+n(a×b)|a×b| along the angle bisector of the vector a and b is
  • l2+m2l2+m2n2
  • 12+m2+n2
  • 12+m2l2m2+n2
  • 1+m2
Let OAB be a regular triangle with side unity (o being otogin). Also M, N are the points of intersection of AB, M being closer to A and N closer to B. Position vectors of A, B, M and N are a,b,m and n respectively. Which of the following hold (s) good ?
  • m=xa+yb23 and y=13
  • m=xa+ybx=56 and y=16
  • m.n equals 1318
  • m.n equals 1518
The position vector of A is 2i+3j+4kAB=5i+7j+6k, then the position vector of B is
  • 7i10j10k
  • 7i10j+10k
  • 7i+10j10k
  • 7i+10j+10k
The position vector of a point lying on the joining the points whose position vectors are ¯i+¯j¯k and ¯i¯j+¯k is
  • ¯j
  • ¯i
  • ¯k
  • ¯0
Area of diagonals is, ..., where diagonals are
a=2ˆi3ˆj+5ˆk, and b=ˆi+ˆj+ˆk
  • 21.5
  • 31.5
  • 28.5
  • 38.5
If ˉa,ˉb,ˉc are position vectors of the points A,B,C respectively such that 9ˉa7ˉb2ˉc=ˉ0 then point B divides AC in the ratio.....
  • Internally 7:2
  • Externally 9:2
  • Internally 9:7
  • Externally 2:7
A vector A=l=xj=3k is rotated through an angle and is also doubled in magnitude resulting inB=4l+(4x2)j+2k. An acceptable value of x is
  • 1
  • 2
  • 3
  • 4/3
A stone projected vertically upwards raises 's' feets in 't' seconds where S=112t16t2 then the maximum height it reached is
  • 195 ft
  • 194 ft
  • 196 ft
  • 216 ft
Given ¯a=xˆi+yˆj+2ˆk,¯b=ˆiˆj+ˆk,¯c=ˆi+2ˆj;(¯a^¯b)=π/2,¯a.¯c=4 then
  • [¯a¯b¯c]2=|¯a|
  • [¯a¯b¯c]=|¯a|
  • [¯a¯b¯c]=0
  • none of these
If a and b are vectors such that |a+b|=29 and a×(2ˆi+3ˆj+4ˆk)=(2ˆi+3ˆj+4ˆk)×b, then
a possible value of (a+b)(7ˆi+2ˆj+3ˆk) is
  • 0
  • 3
  • 4
  • 8
For any three  a,b,c(ab)(bc)×(ca) is equal to
  • b(c×a)
  • 2a(b×c)
  • 0
  • none of these
The point D,E,F divide BC, CA and Ab of the triangle ABC in the ratio 1 : 4, 3 : 2 and 3 : 7 respectively and the point K divides AB in the ratio 1 : 3 then (AD+BE+CF):CK is equal to 
  • 5 : 2
  • 2:5
  • 1:1
  • none of these
(r.i)(r×i)+(r.j)(r×j+)(r.k)(r×k)is equal to
  • 3r
  • r
  • 0
  • None of these
If u = ˆj+4ˆK,V=ˆi3ˆKw=cosθˆi+sinθˆj are vectors in 3- dimensional space, then the maximum possible value of |u×v.w| is 
  • 13
  • 14
  • 5
  • 7
If u = ˆj+4ˆk,V=ˆi=3KandW=cosθi+sinθˆi are vectors in 3-dimension space, then the maximum possible value of |u×v.w| is 
  • 13
  • 14
  • 5
  • 7
If ˆi×(a׈i)+ˆj×(a׈j)+ˆk×(a׈k)=.....{(a.ˆi)ˆi+(a.ˆj)ˆj+(a.ˆk)ˆk}
  • 1
  • 0
  • 2
  • None of these
The magnitude of two vectors which can be represented in the form i+j+(2x)k is 18. Then the unit vector that is perpendicular to these two vectors is
  • i+j2
  • ij82
  • i+j8
  • i+j22
The length of vector AG is
  • 17
  • 51/3
  • 3/6
  • 59/4
For non-zero vectors a,b and c,|(a×b)c|=|a||b||c| holds if and only if
  • ab=0,bc=0
  • bc=0,ca=0
  • ca=0,ab=0
  • ab=bc=ca=0
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers