Question

Find a unit vector in the direction of the vector left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 8 2nd Row 1st Column 7 3rd Row 1st Column negative 2 EndMatrix right bracket

−8
7
−2
.

A unit vector in the direction of the given vector is left bracket Start 3 By 1 Matrix 1st Row 1st Column nothing 2nd Row 1st Column nothing 3rd Row 1st Column nothing EndMatrix right bracket

?
?
?
.

​(Type exact​ answers, using radicals as​ needed.)

Answer 1

`\left[\begin{array}{c}-(8)/(√(117) ) \\(7)/(√(117) )\\(2)/(√(117) )\end{array}\right]`

Explanation:

We are required to find a unit vector in the direction of:

`\left[\begin{array}{c}-8\\7\\2\end{array}\right]`

Unit Vector,
`\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}`

The Modulus of
`\overrightarrow{a}` =
`√((-8)^2+7^2+(-2)^2)=√(117)`

Therefore, the unit vector of the matrix is given as:

`\left[\begin{array}{c}-(8)/(√(117) ) \\(7)/(√(117) )\\(2)/(√(117) )\end{array}\right]`