Question

1.
Two vectors have a sum A and a difference B. If A = B then, the angle
between the two vectors is
(a) 0°
(b) 45°
(c) 120°
(d) 90°​

Answer 1

The angle between the vectors is 90°. hence, the correct option is (d).

Two vectors have a sum A and a difference B.

If A = B then, the angle between the two vectors is..

Let p and q are two vectors and angle between them is Ф.

Sum of p and q is given by,

$A=\sqrt{p^2+q^2+2pqcos\Phi}\:\:....(1)$

Difference of p and q is given by,

$B=\sqrt{p^2+q^2-2pqcos\Phi}\:\:....(2)$

A/C to question,

A = B

$\implies\sqrt{p^2+q^2+2pqcos\Phi}=\sqrt{p^2+q^2-2pqcos\Phi}$

Squaring both sides we get,

⇒ p² + q² + 2pq cosФ = p² + q² - 2pq cosФ

⇒ 4pq cos Ф = 0

⇒ cosФ = 0

⇒ Ф = π/2 or 90°

Therefore the angle between the vectors is 90°. hence, the correct option is (d).

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