Three vectors a, b, and c are given. a = −i + j − k, b = j − k, c = i + j + k

Question

(a) Find their scalar triple product a · (b ⨯ c).

Answer 1

To find a•(bxc) find the cross term first which can be written as a matrix: i j k

0 1 -1

1 1 1

Using minors gives i | 1 +1 | + 1| -j -k|. This gives bxc = 2i -j -k and so a•(bxc) = (-i +j -k)•(2i -j -k) = -2 -1 +1= -2