Question

Find |AXB|
If, |A|=10 , |B|=2, and A.B=12
Please help!

Answer 1

Solution:

There are two Vectors whose cross product is to be calculated

$|\vec A \times \vec B|$

We know that

$|\vec A. \vec B| = |A| |B| cos \: \theta \\ \\ 12 = 10 \times 2 \: cos \: \theta \\ \\ \frac{12}{2 \times 10} = cos \: \theta \\ \\ cos \: \theta = \frac{3}{5} \\ \\ so \\ \\ sin \: \theta = \sqrt{1 - {cos}^{2}\theta } \\ \\ = \sqrt{1 - \frac{9}{25} } \\ \\ sin \: \theta= \frac{4}{5}$
and

$|\vec A \times \vec B| = |A| |B| sin \: \theta \\ \\ = 10 \times 2 \times \frac{4}{5} \\ \\ |\vec A \times \vec B|= 16$

Hope it helps you.

Answer 2

Answer:

There are two Vectors whose cross product is to be calculated

|\vec A \times \vec B|∣

A

×

B

∣