Given the vectors 𝑢⃗ = [1, -4, 2], 𝑣 = [2, 0, -1], and 𝑤⃗ = [-3, -4, -8], evaluate 𝑤⃗ ⋅ 𝑢⃗ × 𝑣 , and state the volume of the parallelepiped defined by these vectors.

Answer 1

i j k

1 -4 2 = 4i+5j+8k = z

2 0 -1

w•z = (-3i-4j-8k)•(4i+5j+8k) =-12-20-64 = -96

Volume = |w•z| = 96 cubic units