Calculating Dot Product Using Components Video Lessons

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Problem: Let vectors A = (2,1,−4), B = (−3,0,1), and C = (−1,−1,2). Calculate the following: A) A⋅B = B) What is the angle θAB between A and B? C) 2B⋅3C = D) 2(B⋅3C) = 

FREE Expert Solution

We are required to perform operations appertaining vector dot product. 

Vector dot product:

A·B=|A|·|B|cosθ

A·B=AxBx+AyBy+AzBz

3D vector Magnitude:

|A|=Ax2+Ay2+Az2

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Problem Details

Let vectors = (2,1,−4), B = (−3,0,1), and = (−1,−1,2). 

Calculate the following: 

A) AB

B) What is the angle θAB between A and B

C) 2B⋅3C

D) 2(B⋅3C)

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