Question

It is found that |A + B| = |A|.This necessarily implies ______.

विकल्प

• B = 0

• A, B are antiparallel

• A, B are perpendicular

• A . B ≤ 0

Answer 1

It is found that |A + B| = |A|.This necessarily implies A, B are antiparallel.

Explanation:

According to the problem,

`|vecA + vecB| = |vecA|`

By squaring both sides, we get

`|vecA + vecB|^2 = |vecA|^2`

⇒ `|vecA|^2 + |vecB|^2 + 2|vecA||vecB| cos theta = |vecA|^2`

Where θ is the angle between `vecA` and `vecB`

`|vecB| (|vecB| + 2|vecA| cos theta)` = 0

⇒ `|vecB| + 2|vecA| cos theta` = 0

⇒ `cos theta = (|vecB|)/(2|vecA|)`

If A and B are antiparallel, then θ = 180°

Hence from equation (i),

`- 1 = (|vecB|)/(2|A|)` ⇒ `|vecB| = 2|vecA|`

Hence, correct answer will be `vecA` and `vecB` are antiparallel provided `|vecB| = 2|vecA|`.

It seem like option (a) is also correct but it is not for `|vecA + vecB| = |vecA|`, either `vecB` = 0 or `vecB = - 2 vecA`, so this option will be false.