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Find the dot product of the vectors shown in the diagram below


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Find the dot product of the vectors shown in the diagram below

 

graph

in Mathematics by ♦ Platinum (97.7k points) | 310 views

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The lengths of the vectors are $$ \|\mathbf{u}\|=1 \text { and }\|\mathbf{v}\|=\sqrt{8}=2 \sqrt{2} $$ and the cosine of the angle $\theta$ between them is $$ \cos \left(45^{\circ}\right)=1 / \sqrt{2} $$ Thus, it follows from Formula (12) that $$ \mathbf{u} \cdot \mathbf{v}=\|\mathbf{u}\|\|\mathbf{v}\| \cos \theta=(1)(2 \sqrt{2})(1 / \sqrt{2})=2 $$
by ♦ Platinum (97.7k points)

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