Question

What is the unit vector that is orthogonal to the plane containing `(29i-35j-17k)` and `(20j +31k)`?

Answer 1

The cross product is perpendicular to each of its factor vectors, and to the plane that contains the two vectors. Divide it by its own length to get a unit vector.

Explanation:

Find the cross product of

`v=29i - 35j - 17k` ... and ... `w=20j+31k`

`v xx w = (29,-35,-17) xx (0,20,31)`

Compute this by doing the determinant `|((i,j,k),(29,-35,-17),(0,20,31))|.`

After you find `v xx w = (a, b, c)=ai+bj+ck,`

then your unit normal vector can be either `n` or `-n` where

`n = (v xx w)/sqrt(a^2+b^2+c^2).`

You can do the arithmetic, right?

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