Question

For two vectors A and B, A + B = A − B is always true when

1. |A| = |B| ≠ 0
2. A ⊥ B
3. |A| = |B| ≠ 0 and A and B are parallel or anti parallel
4. When either |A| or |B| is zero

Answer 1

b and d

Explanation:

Given, `|A + B| = |A - B|`

⇒ `sqrt(|A|^2 + |B|^2 + 2|A||B| cos theta) = sqrt(|A|^2 + |B|^2 - 2|A||B| cos theta)`

⇒ `|A|^2 + |B|^2 + 2|A||B| cos theta = |A|^2 + |B|^2 - 2|A||B| cos theta`

⇒ `4 |A||B| cos theta` = 0

⇒ `|A||B| cos theta` = 0

⇒ `|A|` = 0 or `|B|` = 0 or cos θ = 0

⇒ θ = 90°

When θ = 90°, we can say that A ⊥ B.