Exercise 3.3

]> Exercise 3.3

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Exercise 3.3

Express the square of the component of $\overset{⟶}{v}$ in the direction of $\overset{⟶}{w}$ in terms of dot products.

Solution:

By definition this square is $| \overset{⟶}{v} |^{2} \cos^{2} θ$ where $θ$ is the angle between $\overset{⟶}{v}$ and $\overset{⟶}{w}$ , which is $\frac{{(\overset{⟶}{v}, \overset{⟶}{w})}^{2}}{(\overset{⟶}{w}, \overset{⟶}{w})}$ .