Calculating Dot Product Using Components Video Lessons

Concept

Problem: Find the angle between each of the following pairs of vectors A =Axi + Ayj and B =Bxi + ByjAx3= -4.00, Ay3 = 2.00; Bx3 = 7.00, By3 = 14.00.

FREE Expert Solution

Vector dot product:

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

Vector magnitude:

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

$\begin{array}{rcl}{\mathbf{\theta }}_{{\mathbf{A}}_{\mathbf{3}}{\mathbf{B}}_{\mathbf{3}}}& \mathbf{=}& {\mathbf{cos}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{{\stackrel{\mathbf{⇀}}{\mathbf{A}}}_{\mathbf{3}}\mathbf{·}{\stackrel{\mathbf{⇀}}{\mathbf{B}}}_{\mathbf{3}}}{\mathbf{|}{\stackrel{\mathbf{⇀}}{\mathbf{A}}}_{\mathbf{3}}\mathbf{|}\mathbf{|}{\stackrel{\mathbf{⇀}}{\mathbf{B}}}_{\mathbf{3}}\mathbf{|}}\mathbf{\right)}\end{array}$

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Problem Details

Find the angle between each of the following pairs of vectors =Ax+ Ayj and B =Bx+ Byj

Ax3= -4.00, Ay3 = 2.00; Bx3 = 7.00, By3 = 14.00.