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Q 23.

Expert-verified
Found in: Page 812

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

The dot product is 38 and the angle is ${\mathrm{cos}}^{-1}\left(\frac{38}{\sqrt{2170}}\right)$.

See the step by step solution

## Step 1. Given information.

The given pairs of vectors are:

## Step 2. Find the dot product.

The dot product is: $\mathbit{u}\mathbf{·}\mathbit{v}={u}_{1}{v}_{1}+{u}_{2}{v}_{2}+{u}_{3}{v}_{3}$

Therefore, the dot product of the given two vectors is 38.

## Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

Then,

$\mathrm{cos}\theta =\frac{\mathbit{u}\mathbf{·}\mathbit{v}}{||\mathbit{u}||||\mathbit{v}||}\phantom{\rule{0ex}{0ex}}\mathrm{cos}\theta =\frac{38}{\sqrt{35}\sqrt{62}}\phantom{\rule{0ex}{0ex}}\theta ={\mathrm{cos}}^{-1}\left(\frac{38}{\sqrt{2170}}\right)$

Therefore, the angle is ${\mathrm{cos}}^{-1}\left(\frac{38}{\sqrt{2170}}\right)$.