What is the cross product of [4,-3,2][4,3,2] and [3,1,-5] [3,1,5]?

1 Answer
Dec 14, 2015

=[13, 26, 13]=[13,26,13]

Explanation:

The rule for cross products states that for two vectors, vec a = [a_1, a_2, a_3]a=[a1,a2,a3] and vec b = [b_1, b_2, b_3]b=[b1,b2,b3];

vec a xx vec b = [ a_2b_3-a_3b_2, a_3b_1 - b_3a_1, a_1b_2-a_2b_1 ]a×b=[a2b3a3b2,a3b1b3a1,a1b2a2b1]

For the two vectors given, this means that;

[4, ~3, 2] xx [3, 1, ~5] [4,~3,2]×[3,1,~5]

= [(~3)(~5)-(2)(1), (2)(3) - (~5)(4), (4)(1)-(~3)(3) ]=[(~3)(~5)(2)(1),(2)(3)(~5)(4),(4)(1)(~3)(3)]

=[15-2, 6+20, 4+9]=[152,6+20,4+9]

=[13, 26, 13]=[13,26,13]