# Vectors : Planes, Points, Cross Product and Dot Product

(1) a. Find the (vector) equation of the plane passing through the points (1,2,-2),

(-1,1,-9), (2,-2,-12).

b. Find the (vector) equation of the plane containing (1,2,-1) and perpendicular to

(3,-1,2).

(2) Suppose a, b, c are non zero vectors.

a. Explain why (a x b) x (a x c) is in the direction of a.

b. Show that (a x b) x (a x c ) = ( a . b x c) a.

c. Show that a x b . (b x c) x (c x a) = (a . b x c)Â²

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddfhttps://brainmass.com/math/vector-calculus/vectors-planes-points-cross-product-and-dot-product-12548

#### Solution Summary

A vector equation of a plane is found. Dot and Cross products are calculated. The solution is detailed.

$2.49