If a= <4, -3, 4>, b= <1, 2, -2>, and c= <3, 1, 4>, then the scalar triple product of a, b, and c will be ?

Answer 1

The triple product is equal to a · (b x c). Finding the cross product of b with c is slightly involved, but formulaic. You should be able to look it up in your text book, but for convenience, I believe it would be <(2*4 - 1*-2), (-2*3 - 4*1), (1*1 - 2*3)> = <10, -10, -5>. Then you take the dot product of this vector with a, another straightforward procedure, which yields 4*10 + -3*-10 + 4*-5 = 40 + 30 - 20 = 50. I did this pretty quickly, so it's possible that I made a math error; I'd suggest checking my math as an exercise. This is definitely the correct method, at any rate.