Question

If two vectors `veca` and `vecb` are such that `|veca|` = 2, `|vecb|` = 3 and `veca.vecb` = 4, then `|veca - 2vecb|` is equal to ______.

Options

• `sqrt(2)`

• `2sqrt(6)`

• 24

• `2sqrt(2)`

Answer 1

If two vectors `veca` and `vecb` are such that `|veca|` = 2, `|vecb|` = 3 and `veca.vecb` = 4, then `|veca - 2vecb|` is equal to `underline(bb(2sqrt(6))`.

Explanation:

`|veca - 2vecb|^2 = (veca - 2vecb).(veca - 2vecb)`

`|veca - 2vecb|^2 = veca.veca - 4veca.vecb + 4vecb.vecb`

= `|veca|^2 - 4veca.vecb + 4|vecb|^2`

= 4 – 16 + 36 = 24

`|veca - 2vecb|^2` = 24

⇒ `|veca - 2vecb| = 2sqrt(6)`