Question

57. For two vectors A and B,
->
→ →
| A + B = A - B is always true
when ...
→
(A)| A |=| B|70
->
->
(B) A I B
>
(C)| A =| B|70 and A and B are
parallel
->
(D)|A|=| B|70) and A and B are
anti-parallel​

Answer 1

We know that  A¯¯¯¯×B¯¯¯¯ is perpendicular to both  A¯¯¯¯ and B¯¯¯¯.  

We have

(A¯¯¯¯+B¯¯¯¯)⋅(A¯¯¯¯×B¯¯¯¯)  

=  A¯¯¯¯   ⋅(A¯¯¯¯×B¯¯¯¯)+B¯¯¯¯⋅(A¯¯¯¯×B¯¯¯¯)  

=0+0=0.  

Therefore  A¯¯¯¯+B¯¯¯¯ and A¯¯¯¯×B¯¯¯¯  are perpendicular.

Hence the angle between these vectors is  900.

thank you