Consider the plane which passes through the three points: (6,0,1) ( 6 , 0 , 1 ) , (9,−2,−3) ( 9 , − 2 , − 3 ) , and (9,−1,−1) ( 9 , − 1 , − 1 ) .

Question

Find the vector normal to this plave which has the form (_, 6, _)

Answer 1

Let create vecors u = <9 - 6, -2 - 0, - 3 - 1> = <3, - 2, - 4> and v = <9 - 6, - 1 - 0, - 1 - 1> = <3, -1, - 2>.

Let vector what we looking for x = <a, 6, b>; then x·u = 3a - 12 - 4b = 0 and x·v = 3a - 6 - 2b = 0.

3a - 4b = 12 and 3a - 2b = 6; - 2b = 6, b = - 3 and a = 0.

So, vector x = <0, 6, - 3>