Answer to Question #121888 in Analytic Geometry for Samson

Question

If

α=3i−j+2k,

β=2i+j−k and

γ=i−2j+2k, find

α×β×γ.

Answer 1

Given α=3i-j+2k, β=2i+j−k, y=i-2j+2k.

 

1) First, find the vector product of two vectors using the formula

α х β =i(y1z2- y2 z1)- j(x1z2- x2 z1)+k(x1y2- x2 y1)

Then we get:

α х β =i((-1)(-1)- (1) (2))- j((3)(-1)- (2) (2))+k((3)(1)-( -1)( 2));

α х β =i(1- 2)- j(-3- 4)+k(3+ 2);

α х β =-i+7j+5k;

2) Using the result, we find α х β х y

(α х β )х y= i(y1z2- y2 z1)- j(x1z2- x2 z1)+k(x1y2- x2 y1)

(α х β )х y =i((7)(2)- (5) (-2))- j((-1)(2)- (5) (1))+k((-1)(-2)-( 1)( 7));

(α х β )х y =i(14+10)- j(-2- 5)+k(2-7);

(α х β )х y =24i+7j-5k;