The resultant of two vectors A and B subtends an angle of 45 ∘ with either of them. The magnitude of the resultant is Options: A . &nbspzero B . &nbsp√2A C . &nbspA D . &nbsp2A

The resultant of two vectors A and B subtends an angle of 45∘ with either of

Question

The resultant of two vectors A and B subtends an angle of

45^{\circ}

with either of them. The magnitude of the resultant is

Options:

A . zero

B . √2A

C . A

D . 2A

Answer: Option B
:
B
As shown in figure, the angle

θ

between vectors A and B is

90^{\circ}

.
Also A = B. Therefore, the magnitude of the resultant is given by

R^{2} = A^{2} + B^{2} + 2 A B cos θ

= A^{2} + A^{2} + 2 A^{2} cos 90^{\circ}

= 2 A^{2}

R = \sqrt{2} A .

Hence the correct choice is (b)

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