Let vectors A⃗ = (1,0,-3), B⃗ = (-2,5,1), and C⃗ = (3,1,1). Calculate the following, expressing your answers as ordered triples (three comma-separated numbers).

Answer with explanation:

I have added the required expressions that are needed to be calculated.

B x C = ?

C x B = ?

A. (B x C) = ?

A x (B x C) = ?

Given

A = (1,0,-3)

B = (-2,5,1)

C = (3,1,1)

Using cross product

B x C = (-2,5,1) x (3,1,1) =

i j k

-2 5 1

3 1 1

B x C = i (5 - 1) - j (-2 - 3) + k (-2 - 15) = (4,5,-17)

C x B = (3,1,1) x (-2,5,1) =

i j k

3 1 1

-2 5 1

C x B = i (1 - 5) - j (3 + 2) + k (15 + 2) = (-4,-5,17)

using dot product, we get

A. (B x C) = (1,0,-3). (4,5,-17) = (4,0,51)

Using cross product

A x (B x C) = (1,0,-3) x (4,5,-17) =

i j k

1 0 - 3

4 5 - 17

A x (B x C) = i (0 + 15) - j (-17 + 12) + k (5 - 0) = (15,5,5)