Question

If `|vec"a"| = 8, |vec"b"| = 3 and |vec"a" xx vec"b"|` = 12, then value of `vec"a" * vec"b"` is ______.

Options

• `6sqrt(3)`

• `8sqrt(3)`

• `12sqrt(3)`

• None of these

• `3sqrt(12)`

Answer 1

If `|vec"a"|` = 8, `|vec"b"|` = 3 and `|vec"a" xx vec"b"|` = 12, then the value of `vec"a" * vec"b"` is `underlinebb(12sqrt(3))`.

Explanation:

Using the formula `|vec"a" xx vec"b"| = |vec"a"|*|vec"b"| |sintheta|`

We get `theta = +- pi/6`.

Therefore, `vec"a"*vec"b" = |vec"a"|*|vec"b"| costheta`

= `8 xx 3 xx sqrt(3)/2`

= `12sqrt(3)`.