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Question
For two vectors A and B, A + B = A − B is always true when
- |A| = |B| ≠ 0
- A ⊥ B
- |A| = |B| ≠ 0 and A and B are parallel or anti parallel
- When either |A| or |B| is zero
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Solution
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.
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