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CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 10 - MCQExams.com

Let a=3ˆi+2ˆj+2ˆk,b=ˆi+2ˆj2ˆk. Then a unit vector perpendicular to both ab and a+b is :
  • 13(2ˆi+2ˆj+ˆk)
  • 13(2ˆi+2ˆjˆk)
  • 13(2ˆi2ˆj+ˆk)
  • 13(ˆi+ˆj+ˆk)
If a,b,c are three coplanar vectors, then v[2a+3b,2b5c,2c+3a] is 
  • 0
  • 1
  • 3
  • 3
If x and y be unit vectors and |z|=27 such that z+z×x=y, then the angle θ between x  and z can be 
  • 30
  • 60
  • 90
  • None of these
The position vector of point C with respect to B is  ˉi+ˉj . and that of B with respect to A is ˉi+ˉj.The position vector of C with respect to A is  ____________.
  • 2ˉi
  • 2ˉi
  • 2ˉj
  • 2ˉj
If the vectors 3¯p+¯q:5¯p3¯q and 2¯p+¯q;4¯p2¯q are pairs of mutually perpendicular vectors then sin(¯p¯q) is:

  • 554
  • 558
  • 316
  • 24716
Let ˆa and ˆb two unit vector such that (ˆa.ˆb)2|ˆa׈b| is maximum then |ˆa.ˆb| is equal to
  • 1
  • 13
  • 0
  • 13
The cartesian equation of the plane perpendicular to vector 3ˉi2ˉj2ˉk and passing through the point 2ˉi+3ˉjˉk is
  • 3x+2y+2z=2
  • 3x2y+2z=2
  • 3x+2y2z=2
  • 3x2y2z=2
The position vectors of two vertices and the centroid of a triangle are i+j,2ij+k and k respectively. The position vector of the third vertex of the triangle is :
  • 3i+2k
  • 3i2k
  • i+23k
  • none of these
Unit vector perpendicular to the plane of the triangle  ABC  with position vectors of the vertices  A,B,C,  is  ( where  Δ  is the area of the triangle  ABC ) .
  • (a×b+b×c+c×a)Δ
  • (a×b+¯b×c+c×a)2Δ
  • (a×b+b×c+c×a)3Δ
  • (a×b+b×c+c×a)4Δ
ˉa,ˉb and ˉc are unit vector such that ˉa+ˉbˉc=0. then the angle between ˉa and ˉb is :-
  • π6
  • π3
  • π2
  • 2π3
Let a=(1,2,3) and b=(2,7,4) then
  • a.b=0
  • a.b=9
  • a.b=4
  • a.b=4
If u, v, w are non-coplanar vector and p, q are real numbers, then the equality [3u pv pw][pv w qw][2w qv qu]=0 holds for 
  • Exactly two values of (p, q)
  • More than but not all values of (p, q)
  • All values of (p, q)
  • Exactly one values of (p, q)
If the vectors ¯AB=3ˆi+4ˆk and ¯AC=5ˆi2ˆj+4ˆk are the sides of a triangle ABC, then the length of the median through A is:
  • 18
  • 72
  • 33
  • 45
In the vectors ¯AB=3ˆi+4ˆk and ¯AC=5ˆi2ˆj+4ˆk are the series of a triangle ABC, then the length of the median through A is
  • 18
  • 72
  • 33
  • 45
Let a,b and  c be three non-zero vectors such that no two of them are collinear and (a×b)×c=13|b||c|a. If θ is the angle between vectors b and c, then a value of sinθ is
  • 23
  • 233
  • 223
  • 23
A unit vector d is equally inclined at an angle α with the vectors a=cosθ.i+sinθ.j,b=sinθ.i+cos=θ.j and c=k. Then α is equal to 
  • cos1(12)
  • cos1(13)
  • cos113
  • π2
The foot of the perpendicular drawn from a point with position vector ˆi+4ˆk on the line joining the points ˆj+3ˆk, 2ˆi3ˆj+ˆk is
  • 4ˆi+5ˆj+5ˆk
  • 13(ˆi+ˆj+^8k)
  • 4ˆi+4ˆj5ˆk
  • 4ˆi5ˆj+5ˆk
Let ABCD is a triangular pyramid with base vectors AB=2ˉi+3ˉjˉk and AC=ˉi2ˉk, If volume of the triangular pyramid is 150 unit then its height is
  • 10
  • 20
  • 18
  • 23
If |c| = 60 and c (ˆi + 2ˆj + 5ˆk) = 0 , then a value of c.(7ˆi + 2ˆi + 3ˆk) is :
  • 42
  • 12
  • 24
  • 122
For any vectors a, the value of (a׈i)2+(a׈j)2+(a׈k)2 is equal to?
  • 3a2
  • a2
  • 2a2
  • None of these
The distance of the point P with position vector  3ˆi+6ˆj+8ˆk from y - axis 
  • 62
  • 10
  • 35
  • 73
The adjacent sides of a parallelogram are A=2ˆi3ˆj+ˆk and B=2ˆi+4ˆjˆk What is the area of the parallelogram?
  • 4 units
  • 7 units
  • 5 units
  • 8 units
If  a,b,c  are unit vectors such that  a+b+c=0,  the value of  ab+bc+ca  is
  • 1
  • 3
  • 32
  • None of these
If (ˉaˉb)=¯(a)=¯(b) where ˉa and ˉb are non zero vectors then the angle between ˉaˉb
  • 1200
  • 450
  • 600
  • 900
If the vectors 2ˆi+3ˆj,5ˆi+6ˆj,8ˆi+ λj have their initial point at (1,1)thenthevalueofλ$ so that the vectors terminated on one line is
  • 5
  • 9
  • 4
  • 0
If ¯OP=2ˆi+3ˆjˆk and ¯OQ=3ˆi4ˆj2ˆk then the modulus ¯PQ is
  • 13
  • 51
  • 39
  • 67
From the figure the correct relation is :
1473404_320fae6fd4334bae904853f3976635c7.png
  • ˉA+ˉB+ˉE=ˉ0
  • ˉC+ˉD=¯A
  • ˉB+ˉE+ˉC=¯D
  • All of these
Line passing through (3,4,5) and (4,5,6) has direction ratios
  • 1,1,1
  • 3,3,3
  • 13,13,13
  • 7,9,11
let ˉa,ˉb,ˉc are three mutually perpendicular unit vectors and a unit vector ˉr satisfying the equation (ˉbˉc)×(ˉr×ˉa)+(ˉcˉa)×(ˉr×ˉb)+(ˉaˉb)×(ˉr×ˉc)=0 then ˉr is __________________.
  • 13(ˉa+ˉb+ˉc)
  • 114(2ˉa+3ˉb+ˉc)
  • 114(2ˉa+3ˉb+ˉc)
  • 13(ˉa+ˉb+ˉc)
IfˉA=2ˆi+ˆj+ˆk and ˉB=ˆi+ˆj+ˆk  two vectors,then the unit vector is 
  • Perpendicular to ˉA is ˆj+ˆk2
  • Parallel to ˉA is 2+ˆj+ˆk6
  • Parallel to ˉB is ˆj+ˆk2
  • Parallel to ˆi+ˆj+ˆk3
If x is a vector in the direction of (2,2,1) of magnitude 6 and y is a vector in the direction of (1,1,1) of magnitude 3, then |x+2y|=...
  • 40
  • 35
  • 17
  • 210
The position vector of a point P is r=xi+yj+xk, Where x,y,z,ϵN and a=i+j+k. If r.a=10, then the number of possible positions of P is ___________.
  • 30
  • 72
  • 66
  • 36
Let ¯a=4ˆi+3ˆjˆk and¯b=2ˆi6ˆj3ˆk. Then a unit vector to both ¯a and ¯bis.
  • 17(3ˆi2ˆj+3ˆk)
  • 17(3ˆi+2ˆj6ˆk)
  • 17(3ˆi+2ˆj6ˆk)
  • 17(3ˆi+2ˆj6ˆk)
If a=ˆi+2ˆj+2ˆk and b=2ˆi+ˆj+2ˆk. Find the projection vector of b on a.
  • 89(ˆi+2ˆj+2ˆk)
  • 89(2ˆi+ˆj+2ˆk)
  • 98(ˆi+2ˆj+2ˆk)
  • 98(2ˆi+ˆj+2ˆk)
Unit vector perpendicular to vector  A=3ˆi2ˆj3ˆk  and  B=2ˆi+4ˆj+6ˆk  both is
  • 3ˆj2ˆk13
  • 3ˆk2ˆj13
  • ˆj+2ˆk13
  • ˆi+3ˆjˆk13
If the position vector a of point (12,n) is such that |a|=13, then find the value (s) of n.
  • ±6
  • ±4
  • ±5
  • ±7
Express AB in terms of unit vectors ˆi and ˆj, when the points are:
A(4,-1), B(1,3)
Find |AB| in each case.
  • AB=3ˆi4ˆj,|AB|=5
  • AB=+3ˆi+4ˆj,|AB|=5
  • AB=3ˆi+4ˆj,|AB|=5
  • none of these
What is the scalar projection of 
a=ˆi+2ˆj+ˆk on b=4ˆi+4ˆj+7ˆk ?
  • 69
  • 199
  • 919
  • 619
If a,b,c are vectors such that a+b+c=0 and |a|=7,|b|=5,|c|=3, then the angle between c and b is
  • π3
  • π6
  • π4
  • π
If a unit vector a makes an angle π3 with ˆi,π4 with ˆj and an accute angle θ with ˆk, then find θ and hence, the components of a.

  • π3;a=12ˆi12ˆj+12ˆk
  • π3;a=12ˆi+12ˆj+12ˆk
  • π3;a=12ˆi+12ˆj+12ˆk
  • π3;a=12ˆi+12ˆj12ˆk
The adjacent sides of a parallelogram are represented by the vectors a=ˆi+ˆj+ˆk and b=2ˆi+ˆj+2ˆk. Find unit vectors parallel to the diagonals of the parallelogram.


  • 12(ˆi+2ˆj+ˆk),16(ˆi+ˆk)
  • 12(ˆi+2ˆj+ˆk),16(ˆiˆk)
  • 122(3ˆi+2ˆj+3ˆk),12(ˆi+ˆk)
  • 12(+ˆi+2ˆj+ˆk),16(ˆiˆk)
The unit vector normal to the plane containing a=(ˆiˆjˆk) and b=(ˆi+ˆj+ˆk) is?
  • (ˆjˆk)
  • (ˆj+ˆk)
  • 12(ˆj+ˆk)
  • 12(ˆi+ˆk)
Let a=2ˆiˆj+ˆk,b=ˆi+2ˆjˆk and c=ˆi+ˆj2ˆk be three vectors. A vector in the plane of b and c whose projection on a is of magnitude (2/3) is
  • 2ˆi+3ˆj3ˆk
  • 2ˆi+3ˆj+3ˆk
  • 2ˆiˆj+5ˆk
  • 2ˆi+ˆj+5ˆk
If ˉa and ˉb=3ˆi+6ˆj+6ˆk are collinear and ˉa.ˉb=27, then ˉa is equal to 
  • 3(ˆi+ˆj+ˆk)
  • ˆi+2ˆj+2ˆk
  • 2ˆi+2ˆj+2ˆk
  • ˆi+3ˆj+3ˆk
  • ˆi3ˆj+2ˆk
Let O be the circumcentre, G be the centroid and O be the orthocentre of a ABC. Three vectors are taken through O and are represented by a=OA,b=OB and c=OC then a+b+c is
  • OG
  • 2OG
  • OO
  • None of them
If (a×b)2+(a.b)2=144 and |a|=4, then |b|=
  • 16
  • 8
  • 3
  • 12
A parallelogram is constructed on the vectors
a=3αβ,b=α+3β if |α|=|β|=2 and angle between α and β is π/3 then the length of a diagonal of the parallelogram is
  • 45
  • 43
  • 47
  • None of these
A,B,C and D have position vectors a,b,c and d respectively, such that ab=2(dc). Then
  • AB and CD bisect each other
  • BD and AC bisect each other
  • AB and CD trisect each other
  • BD and AC trisect each other
pˆi+3ˆj+4ˆk and qˆi+4ˆk are two vectors, where p,q>0 are two scalars, then the length of the vectors is equal to
  • All value of (p,q)
  • Only finite number of values of (p,q)
  • Infinite number of values of (p,q)
  • No value fo (p,q)
(r.ˆi)(r׈i)+(r.ˆj)(r׈j)+(r.ˆk)(r׈k) is equal to
  • 3 r
  • r
  • 0
  • None of these
0:0:1


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