Question

Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.

Answer 1

`vXw =-36i+33j+26k`

Explanation:

v = 3i + 8j – 6k

w = –4i – 2j – 3k

The cross product

`v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|`

`=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\`

`=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k`