Find the length and direction of $u\times v$ and $v\times u$

u = 2i - 2j + 4k, v = -i + j - 2k

u = 2i - 2j + 4k, v = -i + j - 2k

przesypkai4
2022-07-30
Answered

Find the length and direction of $u\times v$ and $v\times u$

u = 2i - 2j + 4k, v = -i + j - 2k

u = 2i - 2j + 4k, v = -i + j - 2k

You can still ask an expert for help

kuglatid4

Answered 2022-07-31
Author has **12** answers

First we find $u\times v=\left|\begin{array}{ccc}i& j& k\\ 2& -2& 4\\ -1& 1& -2\end{array}\right|$

=i(4-4)-j(-4+4)+k(2-2)

=0

and $v\times u=\left|\begin{array}{ccc}i& j& k\\ -1& 1& -2\\ 2& -2& 4\end{array}\right|$

=i(4-4)-j(-4+4)+k(2-2)

=0

$\therefore $ The length of the $u\times v$ and$v\times u$ is'zero', and both are have the same direction.

=i(4-4)-j(-4+4)+k(2-2)

=0

and $v\times u=\left|\begin{array}{ccc}i& j& k\\ -1& 1& -2\\ 2& -2& 4\end{array}\right|$

=i(4-4)-j(-4+4)+k(2-2)

=0

$\therefore $ The length of the $u\times v$ and$v\times u$ is'zero', and both are have the same direction.

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