Question

If `|overset->a|` = 3, `|overset->b|` = 4 and `|overset->a + overset->b|` = 5, then `|overset->a - overset->b|` = ______.

Options

• 3

• 4

• 5

• 8

Answer 1

If `|overset->a|` = 3, `|overset->b|` = 4 and `|overset->a + overset->b|` = 5, then `|overset->a - overset->b|` = 5.

Explanation:

`|overset->a|` = 3, `|overset->b|` = 4 and `|overset->a + overset->b|` = 5

We have `|overset->a + overset->b|^2 + |overset->a - overset->b|^2`

= `2(|overset->a|^2 + |overset->b|^2)`

= 2(9 + 16)

= 50

`⇒ |overset->a - overset->b| = 5`