If \(\overrightarrow{\mathbf{A}}{=}{2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{\mathbf{B}}{=}\hat{i}{-}\hat{j}\) , then the components of A along with B & perpendicular to B respectively will be:
1.  i^-j^2, 32i^+j^

2.  i^-j^2,- 23i^+j^

3.  i^-j^2, -32i^-j^

4.  i^-j^2, 23i^-j^

Subtopic:  Scalar Product |
 54%
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If \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)

Subtopic:  Scalars & Vectors |
From NCERT
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If \(\theta\) is the angle between two vectors a and b, and |a×b|=a.b, then \(\theta\) is equal to:
1. \(0^\circ\)
2. \(180^\circ\)
3. \(135^\circ\)
4. \(45^\circ\)

Subtopic:  Vector Product |
 75%
From NCERT
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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-

1.  (1, 1/2, -1/2)

2.  (2/3, 1/3, -1/3)

3.  (1/2, 1/4, -1/4)

4.  (1, 1, 0)

Subtopic:  Scalar Product |
 53%
From NCERT
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If a, b and c are three non-zero vectors such that a+b+c=0, then the value of a.b+b.c+c.a will be:

1.  Less than zero

2.  equal to zero

3.  greater than zero

4.  3

Subtopic:  Scalar Product |
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Two vectors a and b inclined at an angle θ with respect to 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

Subtopic:  Resultant of Vectors |
 69%
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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

(1)  can be zero

(2)  cannot be zero

(3)  lies in the plane of A &B

(4)  lies in the plane of A & A+B

Subtopic:  Resultant of Vectors |
 64%
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The vector sum of the forces of 10 N and 6 N can be

(1)  2 N

(2)  8 N

(3)  18 N

(4)  20 N

Subtopic:  Resultant of Vectors |
 85%
From NCERT
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A set of vectors taken in a given order gives a closed polygon. Then the resultant of these vectors is a 

(1)  scalar quantity

(2)  pseudovector

(3)  unit vector

(4)  null vector

Subtopic:  Resultant of Vectors |
 72%
From NCERT
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The vector sum of two vectors P and Q is minimum when the angle θ between their positive directions, is

(A)  π4

(B)  π3

(C)  π2

(D)  π

Subtopic:  Resultant of Vectors |
 68%
From NCERT
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