Calculating X,Y, and Z Components? Mastering Physics?

Anyone willing to help I would appreciate it! I am currently lost in this section so any help would be great!!

Let vectors A⃗ =(2,−1,1), B⃗ =(3,0,5), and C⃗ =(1,4,−2), where (x,y,z) are the components of the vectors along i, j, and k respectively. Calculate the following:

A. 2A⃗ +3B⃗ +C⃗

B. |A⃗ |,|B⃗ |,|C⃗ |

C. A⃗ ⋅B⃗

D. Determine the angle θ between B⃗ and C⃗

E. B⃗ ×C⃗

F. A⃗ ⋅(B⃗ ×C⃗ ) =

Answer:

A. 2A⃗ +3B⃗ +C⃗ = (2*2+3*3+1, 2*-1+3*0+4, 2*1+3*5+-2) = (14, 2, 15)

B. |A⃗ |,|B⃗ |,|C⃗ |

|A| = √(2² + (-1)² + 1²) = √6

I’ll leave |B| and |C| for you

C. A⃗ ⋅B⃗ = 2*3 + -1*0 + 1*5 = 11

D. Determine the angle θ between B⃗ and C⃗

Θ = arccos(A•B / |A||B|)

A•B was done in part C. |A| was done in part B. Find |B| and you’re golden.

E. B⃗ ×C⃗ = (0*-2-5*4, 5*1-3*-2, 3*4-0*1) = (-20, 11, 12)

F. A⃗ ⋅(B⃗ ×C⃗ ) = 2*-20 – 1*11 + 1*12 = -39

assuming part E is correct.

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