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Expert-verified Found in: Page 812 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # In Exercises 24-27, find ${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}\mathbf{},{\mathrm{proj}}_{\mathbf{u}}\mathbf{v}$ and the component of v orthogonal to u.

The values are and the component of v orthogonal to u is .

See the step by step solution

## Step 1. Given information.

The given vectors are:

## Step 2. Find the component of the projection of v onto u.

Then,

${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=\frac{\mathbit{u}\mathbf{·}\mathbit{v}}{||\mathbit{u}||}\phantom{\rule{0ex}{0ex}}=\frac{-1}{\sqrt{29}}$

Therefore, localid="1649675490199" ${\mathrm{comp}}_{\mathbf{u}}\mathbf{v}=\frac{-1}{\sqrt{29}}$.

## Step 3. Find the vector projection of v onto u.

Therefore, the vector projection of v onto u is .

## Step 4. Find the component of v orthogonal to u.

The component of v orthogonal to u is $\mathbf{v}-{\mathrm{proj}}_{\mathbf{u}}\mathbf{v}$.

Therefore, the component of v orthogonal to u is . ### Want to see more solutions like these? 