Question

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 1

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)