Question

The vectors A and B are such that A+ B = A-B . The angle between the two vectors is
(A) 75°
(B) 450
(C) 90°
(D) 60°​

Answer 1

HERE IS YOUR ANSWER :-

OPTION (C) IS CORRECT

Answer 2

Answer:

The angle between the two vectors is 90°.i.e.option (C).

Explanation:

As per the question,

        A+B=A-B      (1)

Equation (1) states that their resultant is the same. So, first, let's find the resultant of A+B i.e.

$R_1=\sqrt{A^2+B^2+2ABcos\theta}$         (2)

Now let's find the resultant of the vectors A-B i.e.

$R_2=\sqrt{A^2+B^2-2ABcos\theta}$         (3)

From equation (1) we have,

 ∴    $R_1=R_2$

So,

$A^2+B^2+2ABcos\theta=A^2+B^2-2ABcos\theta$

$4ABcos\theta=0$

$cos\theta=90\textdegree$

Hence, the angle between the two vectors is 90°.i.e.option (C).