If A=2i^+j^ & B=i^-j^ . Find component of A along B & perpendicular to B.

1.  i^-j^2, 32i^+j^

2.  i^-j^2,- 23i^+j^

3.  i^-j^2, -32i^-j^

4.  i^-j^2, 23i^-j^

Concept Questions :-

Resolution of vectors
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If a is a vector and x is a non-zero scalar, then

(A) xa is a vector in the direction of a

(B)  xa is a vector collinear to a

(C)  xa and a have independent directions

(D)  xa is a vector perpendicular to a

Concept Questions :-

Scalar Product
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A vector that is perpendicular to both the vectors a=i^-2j^+k^ and b=i^-j^+k^ is

(A)  -i^+k^

(B)  -i^-2j^+k^

(C)  i^-2j^+k^

(D)  i^+k^

Concept Questions :-

Scalar Product
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If θ is the angle between vectors a and b, and |a×b|=a.b, then θ is equal to

(A)  0°

(B)  180°

(C)  135°

(D)  45°

Concept Questions :-

Vector Product
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The vector b, which is collinear with the vector a=(2, 1, -1) and satisfies the condition a.b=3, is 

(A)  (1, 1/2, -1/2)

(B)  (2/3, 1/3, -1/3)

(C)  (1/2, 1/4, -1/4)

(D)  (1, 1, 0)

Concept Questions :-

Scalar Product
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If 3i^+2j^+8k^ and 2i^+xj^+k^ are at right angle then x=

(A)  7

(B)  -7

(C)  5

(D)  -4

Concept Questions :-

Scalar Product
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If a, b, c are three non-zero vectors such that a+b+c=0 the value of a.b+b.c+c.a is

(A)  Less than zero

(B)  equal to zero

(C)  greater than zero

(D)  3

Concept Questions :-

Scalar Product
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Let α, β, γ be distinct real numbers. The points with position vectors αi^+βj^+γk^ , βi^+γj^+αk^ , γi^+αj^+βk^

(A)  are collinear

(B)  from an equilateral triangle

(C) form an isosceles triangle

(D)  from a right angled triangle

Concept Questions :-

Resultant of Vectors
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Two vectors a and b inclined at an angle θ w.r.t. each other have a resultant c which makes an angle β with a. If the directions of a and b are interchanged, then the resultant will have the same

(A)  magnitude

(B)  direction

(C)  magnitude as well as direction

(D)  neither magnitude nor direction

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Two vectors A and B lie in a plane. Another vector C lies outside this plane. The resultant A+B+C of these three vectors

(A)  can be zero

(B)  cannot be zero

(C)  lies in the plane of A &B

(D)  lies in the plane of A & A+B

Concept Questions :-

Resultant of Vectors
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