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Q 23.

Expert-verifiedFound in: Page 812

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.

$\mathit{u}=>">-5,1,3$

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

The given pairs of vectors are:

$\mathit{u}=>">-5,1,3$

The dot product is: $\mathit{u}\mathbf{\xb7}\mathit{v}={u}_{1}{v}_{1}+{u}_{2}{v}_{2}+{u}_{3}{v}_{3}$

$\mathit{u}=>">-5,1,3$

Therefore, the dot product of the given two vectors $\mathit{u}=>">-5,1,3$ is 38.

The formula for the angle between the two vectors is:

$\mathrm{cos}\theta =\frac{\mathit{u}\mathbf{\xb7}\mathit{v}}{||\mathit{u}||||\mathit{v}||}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathit{u}=>">-5,1,3$

Then,

$\mathrm{cos}\theta =\frac{\mathit{u}\mathbf{\xb7}\mathit{v}}{||\mathit{u}||||\mathit{v}||}\phantom{\rule{0ex}{0ex}}\mathrm{cos}\theta =\frac{38}{\sqrt{35}\sqrt{62}}\phantom{\rule{0ex}{0ex}}\theta ={\mathrm{cos}}^{-1}\left(\frac{38}{\sqrt{2170}}\right)$

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

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