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

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

Answer 1

Answer:

$\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]$

Step-by-step 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, $\hat{a}=\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}$

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

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

$\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]$