Question

If `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12, then value of `|vec"a" xx vec"b"|` is ______.

Options

• 5

• 10

• 14

• 16

Answer 1

If `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12, then value of `|vec"a" xx vec"b"|` is 16.

Explanation:

Given that `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12

∴ `vec"a" . vec"b" = |vec"a"||vec"b"| cos theta`

⇒ 12 = `10 * 2 * cos theta`

⇒ `cos theta = 12/20 = 3/5`

∴ `sin theta = sqrt(1 - cos^2theta)`

⇒  `sin theta = sqrt(1 - (3/5)^2`

⇒ `sin theta = sqrt(1 - 9/25)`

⇒ `sin theta = sqrt(16/25)`

⇒ `sin theta = 4/5`

Now `|vec"a" xx vec"b"| = |vec"a"| |vec"b"| sin theta`

= `10 * 2 * 4/5`

= 16