Calculating Dot Product Using Components Video Lessons

Concept

# 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:

$\overline{)\stackrel{\mathbf{⇀}}{\mathbf{A}}{\mathbf{·}}\stackrel{\mathbf{⇀}}{\mathbf{B}}{\mathbf{=}}{\mathbf{|}}\stackrel{\mathbf{⇀}}{\mathbf{A}}{\mathbf{|}}{\mathbf{·}}{\mathbf{|}}\stackrel{\mathbf{⇀}}{\mathbf{B}}{\mathbf{|}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$

$\overline{){\mathbf{A}}{\mathbf{·}}{\mathbf{B}}{\mathbf{=}}{{\mathbf{A}}}_{{\mathbf{x}}}{{\mathbf{B}}}_{{\mathbf{x}}}{\mathbf{+}}{{\mathbf{A}}}_{{\mathbf{y}}}{{\mathbf{B}}}_{{\mathbf{y}}}{\mathbf{+}}{{\mathbf{A}}}_{{\mathbf{z}}}{{\mathbf{B}}}_{{\mathbf{z}}}}$

3D vector Magnitude:

$\overline{)|\stackrel{⇀}{\mathbit{A}}|{=}\sqrt{{{\mathbit{A}}_{\mathbit{x}}}^{2}+{{\mathbit{A}}_{\mathbit{y}}}^{2}+{{\mathbit{A}}_{\mathbit{z}}}^{2}}}$

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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)