# Given two vectors, find vector of the parallelogram height

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1. Apr 5, 2015

### AndrejN96

1. The problem statement, all variables and given/known data
Find the coordinates of the vector of the height of the parallelogram formed by vectors a={1, 2, 1} and b={2, -1, 0}

2. Relevant equations
A=|axb|, A=|a|*h

3. 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.

2. Apr 5, 2015

### Staff: Mentor

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

3. Apr 7, 2015

### ehild

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