Calculating Dot Product Using Components Video Lessons

Concept

# Problem: Find the angle between the following pair of vectors A = Ax î + Ay ĵ and B = Bx î + By ĵ.Ax1 = -2.20, Ay1 = 6.60; Bx1 = 2.00, By1 = -2.30.

###### 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:

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

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

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###### Problem Details

Find the angle between the following pair of vectors A = Ax î + Ay  and B = Bx î + By .

Ax1 = -2.20, Ay1 = 6.60; Bx1 = 2.00, By1 = -2.30.