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

1 Answer
Feb 9, 2016

Answer:

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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