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CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 5 - MCQExams.com

A man starts from O moves 500m turns by 60 and moves 500m again turns by 60 and moves 500m and so on. Find the displacement after (i) 5th turn , (ii) 3rd turn.
  • -500m,1000m
  • 500m,5003m
  • 1000m,5003m
  • none of these
The projection of the vector ˆi2ˆj+ˆk on the vector 4ˆi4ˆj+7ˆk is
  • 5610
  • 199
  • 919
  • 619
If the vector product of a constant vector OA with a variable vector OB in a fixed plane OAB be a constant vector, then locus of B is :
  • A straight line perpendicular to OA
  • A circle with centre O radius equal to |OA|
  • A straight line parallel to OA
  • None of these
There are N co-planar vectors each of magnitude VEach vector is inclined to the preceding vector at angle 2π/N. What is the magnitude of their resultant?

  • zero
  • V/N
  • V
  • NV
P,Q have position vectors ab relative to the origin 'O' and X,Y  divide PQ intermally and extemally respectively in the ratio 2:1, then vector XY=
  • 32(ba)
  • 43(ca)
  • 56(ba)
  • 43(ba)
If . and × represent dot product and cross product respectively then which of the following is meaningless?
  • (a×b).(c×d)
  • (a×b)×(c×d)
  • (a.b).(c×d)
  • (a.b)×(c×d)
If a.b=0 and a×b=0 then
  • ab
  • ab
  • a=0 or b=0
  • None of these
If G and G be the centroids of the triangles ABC and ABC respectively, then AA+BB+CC=
  • 23GG
  • GG
  • 2GG
  • 3GG
Five coplanar forces of equal magnitudes 10N each, act at a point such that the angle between any two consecutive forces is same. The magnitude of their resultant is :
  • 0
  • 10N
  • 20N
  • 102N
P is a point on the line through the point A whose position vector is a and the line is parallel to the vector b. If PA=6, the position vector of P is
  • a+6b
  • a+6|b|b
  • a6b
  • b+6|a|a
A straight line r=a+λb meets the plane r.n=0 in P. The position vector of P is
  • a+a.nb.nb
  • a+b.na.nb
  • aa.nb.nb
  • None of these
Let AB=3ˆi+ˆjˆk and AC=ˆiˆj+3ˆk. If the point P on the line segment BC is equidistant from AB and AC then AP is
  • 2ˆiˆk
  • ˆi2ˆk
  • 2ˆi+ˆk
  • None of these
If the vectors a, b, c and d are coplanar, then (a×b)×(c×d) is equal to
  • a+b+c+d
  • 0
  • a+b=c+d
  • None of these
If a, b, c, d are any four vectors then (a×b)×(c×d) is a vector
  • Perpendicular to a, b, c, d
  • Along the line of intersection of two planes, one containing a, b and the other containing c, d
  • Equally inclined to both a×b and c×d
  • None of these
The position vectors of two vertices and the centroid of a triangle are i+j, 2ij+k and k respectively, then the position vector of the third vertex of the triangle is 
  • 3i+2k
  • 3i2k
  • i+23k
  • None of these
R(ˉr) is any point on a semi-circle, P(ˉp) and Q(ˉq) are the position vector of the end point of the diameter of that semi-circle, then ¯PR¯QR is equal to
  • 1
  • 0
  • 3
  • Not defined
In a triangle OAB, E is the mid-point of OB and D is a point on AB such that AD: DB = 2 :If OD and AE intersect at P, determine the ratio OP : PD using vector methods.
  • OP:PD=2:3
  • OP:PD=3:2
  • OP:PD=1:3
  • OP:PD=3:1
In a triangle ABC, D divides BC in the ratio 3 : 2 and E divides CA in the ratio 1 :The lines AD and BE meet at H and CH meets AB in F. Find the ratio in which F divides AB.
  • AF:FB=2:1
  • AF:FB=1:2
  • AF:FB=2:3
  • AF:FB=3:2
ˉa=xˆi+yˆj+zˆk,ˉb=ˆj then the vector ˉc for which ˉa,ˉb,ˉc form a right hand triad
  • x(ˆiˆk)
  • ˉ0
  • zˆi+xˆk
  • yˆj
Let ˉp and ˉq be two distinct points. Let R and S be the points dividing PQ internally and externally in the ratio 2:3. If ¯OR¯OS, then
  • 9p2=4q2
  • 4p2=9q2
  • 9p=4q
  • 4p=9q
The difference of the squares on the diagonals is four times the rectangle contained by either of these sides and the projection of the other upon it.
  • =4 ( rectangle contained by AB and projection of AC on AB).
  • =1 ( rectangle contained by AB and projection of AC on AB).
  • =8 ( rectangle contained by AB and projection of AC on AB).
  • =2 ( rectangle contained by AB and projection of AC on AB).
State true or false:
The four diagonals of a parallelopiped and the joins of the mid-points of opposite edges are concurrent at a common point of bisection.
  • True
  • False
ABC is a Δ and G is its centroid. If ¯AB=ˉb and ¯AC=ˉc, then ¯AG is equal to
  • 23(ˉb+ˉc)
  • ˉb+ˉc
  • 13(ˉb+ˉc)
  • 32(ˉb+ˉc)
In a parallelogram ABCD,|AB|=a,|AD|=b and |AC|=c. Then, DB.AB has the value
  • 3a2+b2c22
  • a2+3b2c22
  • a2b2+3c22
  • a2+3b2+c22
Let ˉa, ˉb and ˉc be vectors with magnitudes 3,4 and 5 respectively and ˉa+ˉb+ˉc=0, then the value of ˉa.ˉb+ˉb.ˉc+ˉc.ˉa is
  • 48
  • 26
  • 25
  • 25
The sides of a are in A.P, then the line joining the centroid to the incenter is parallel to
  • The largest side
  • The middle side
  • The smallest side
  • None of these
If ˉα, ˉβ and ˉγ be vertices of a whose circumcenter is at the origin, then orthocenter is given by
  • ˉα+ˉβ+ˉγ4
  • ˉα+ˉβ+ˉγ2
  • ˉα+ˉβ+ˉγ
  • ˉα+ˉβ+ˉγ3
If S is the circumcenter, O is the orthocenter of ABC, then SA+SB+SC=
  • 2OS
  • 2SO
  • OS
  • SO
For non-zero vectors ˉa, ˉb and ˉc, |(ˉa×ˉb).ˉc|=|ˉa||ˉb||ˉc| iff
  • ˉa.ˉc=0, ˉa.ˉb=0
  • ˉa.ˉb=0, ˉb.ˉc=0
  • ˉc.ˉa=0, ˉb.ˉc=0
  • ˉa.ˉb=ˉb.ˉc=ˉc.ˉa=0
Two planes are perpendicular to each other,one of them contains vector ˉa and ˉb, other contains ˉc and ˉd then (ˉa×ˉb)(ˉc×ˉd)=
  • 1
  • 0
  • [ˉaˉbˉc]
  • [ˉbˉcˉd]
Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then ¯OA+¯OB+¯OC+¯OD=
  • 2¯OP
  • 3¯OP
  • ¯OP
  • 4¯OP
If a. b0, find the vector r which satisfies the equations (rc)×b=0,r.a=0
  • r=(a.b)c+(a.c)ba.b
  • r=(a.b)c(a.c)ba.b
  • r=(a.b)c(a.c)ba.b
  • r=(a.b)c+(a.c)ba.b
If αˉa+βˉb+γˉc=0, then (ˉa×ˉb)×[(ˉb×ˉc)×(ˉc×ˉa)] is equal to
  • ˉ0
  • A vector plane of ˉa, ˉb and ˉc
  • A scalar quantity
  • None of these
A unit vector perpendicular to each of the vectors 2ˆi+4ˆjˆk and ˆi2ˆj+3ˆk forming a right handed system is
  • 7ˆi10ˆj+8ˆk
  • 10ˆi7ˆj8ˆk213
  • 7ˆi+10ˆj+8ˆk
  • 10ˆi7ˆj8ˆk213
The position vector of the points A and B are respectively ˉa and ˉb  divides AB in the ratio 3:1 and Q iis the midpoint of AP. The position vector of Q is
  • 3ˉa+5ˉb8
  • 3ˉa+ˉb4
  • ˉa+3ˉb4
  • 5ˉa+3ˉb8
For three unit vectors ˉaˉb and ˉcif ˉa+ˉb+ˉc=ˉ0, then the value of ˉa(ˉb+ˉc)+ˉb(ˉc+ˉa)+ˉc(ˉa+ˉb) is equal to
  • 32
  • 0
  • 3
  • None of these
If ˉa×ˉb=ˉb×ˉc=ˉc×ˉa then ˉa+ˉb+ˉc=?
  • abc
  • 1
  • 0
  • 2
The vector (ˉa×ˉb)×(ˉc×ˉb) is
  • At right angle to ˉb
  • Is parallel to ˉc
  • Is parallel to ˉb
  • None of these
In a trapezium the vector ¯BC=α¯AD. We will then find that ˉp=¯AC+¯BD is collinear with ¯AD. if ˉp=μ¯AD then
  • μ=α+2
  • μ+α=2
  • α=μ+1
  • μ=α+1
If C is the mid point of AB and P is any point outside AB, then
  • ¯PA+¯PB+¯PC=0
  • ¯PA+¯PB+2¯PC=ˉ0
  • ¯PA+¯PB=¯PC
  • ¯PA+¯PB=2¯PC
Given A=ai+bj+ck, B=di+3j+4k and C=3i+j2k. If the vectors A,B and C form a triangle such that A=B+C and area(ΔABC)=56, then
  • a=8, b=4, c=2, d=11
  • a=8, b=4, c=2, d=11
  • a=8, b=4, c=2, d=11
  • None of the above
Two identical particles are located at x and y with reference to the origin of three dimensional co-ordinate system. The position vector of centre of mass of the system is given by
  • xy
  • x+y2
  • (xy)
  • xy2
A vector a can be written as
  • (ai)i+(aj)j+(ak)k
  • (aj)i+(ak)j+(ai)k
  • (ak)j+(ai)j+(aj)k
  • (aa)i+(i+j+k)k
If b0, then every vector a can be written in a unique manner as the sum of a vector a|| parallel to b and a vector a perpendicular to b. If a is parallel to b, then a||=a and a=0. If a is perpendicular to b, then a||=0 and a=a. The vector a|| is called the projection of a on b and is denoted by projba. Since projba is parallel to b, it is a scalar multiple of the unit vector in the direction of b, i.e., projba=λub
The scalar λ is called the component of a in the direction of b and is denoted by compba. In fact, projba=(aub)ub and compba=aub

If a=2i+j+k and b=4i3j+k, then projba is equal to
  • 4i3j+2k
  • 513(4i3j+k)
  • 513(4i3j+k)
  • 411(2ij+2k)
ABCD is a quadrilateral and E the point of intersection of the lines joining the middle points of opposite sides. If O is any point, then the resultant of OA,OB,OC and OD is equal to
  • 2OE
  • OE
  • 4OE
  • none of these
The components of vector i+j+k along vector i+2j+3k is
  • (3/7)(i+2j+3k)
  • (i+2j+3k)
  • (1/7)(i+2j+3k)
  • (4/7)(i+2j+3k)
Four forces of magnitude P, 2P, 3P and 4P act along the four sides of a square ABCD in cyclic order. Use the vector method to find the resultant force.
  • 22P
  • 32P
  • 2P
  • 22P
OAB is a given triangle such that OA=ˉa, OB=ˉb.
Also C is a point on AB such that AB=2BC. State which of the following statements are correct?
  • AC=23(ˉbˉa),
  • AC=23(ˉaˉb),
  • AC=23(ˉb+ˉa),
  • AC=32(ˉbˉa),
ABC is any triangle and D,E,F are the middle points of its sides BC,CA,AB respectively. Express the vectors CF and BE as linear combination of the vectors AB and AC
  • BE=12ACAB;CF=12ABAC
  • BE=12AC+AB;CF=12AB+AC
  • CF=12ACAB;BE=12ABAC
  • CF=12AC+AB;BE=12AB+AC
If A(a),B(b),C(c) be the vertices of a triangle whose circumcentre is the origin, then orthocenter is given by
  • a+b+c3
  • a+b+c2
  • a+b+c
  • None of these
0:0:2


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Practice Class 12 Commerce Maths Quiz Questions and Answers