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:

Part A

Express your answer as an ordered triplet of components (x,y,z) with commas to separate the components.

2A⃗ +3B⃗ +C⃗ =

Part B

Express your answer as an ordered triplet |A⃗ |,|B⃗ |,|C⃗ | with commas to separate the magnitudes.


|A⃗ |,|B⃗ |,|C⃗ | =

Part C

A⃗ ⋅B⃗ =

Part D

Determine the angle θ between B⃗ and C⃗.

Express your answer numerically in radians, to two significant figures.


θ =

radians

Part E

Express your answer as an ordered triplet of components (x,y,z) with commas to separate the components.

B⃗ ×C⃗ =

Part A⃗ ⋅(B⃗ ×C⃗ ) =