Given two vectors, find vector of the parallelogram height

[AndrejN96]

Homework Statement

Find the coordinates of the vector of the height of the parallelogram formed by vectors a={1, 2, 1} and b={2, -1, 0}

Homework Equations

A=|axb|, A=|a|*h

The Attempt at a Solution

I can find the intensity of the vector h i.e the length of the height, but not its vector. I know the dot product of a and h is zero, but that's it. I'm stuck.

 

[mfb]

axb is orthogonal to both a and h, you can use this vector to find h.

 

[ehild]

$\vec p$ is the projection of $\vec a$ onto the direction of $\vec b$ , and $\vec h = \vec a - \vec p$