Linear Algebra Examples

$(1, 3)$

Step 1

To find a unit vector in the same direction as a vector $v⃗$ , divide by the norm of $v⃗$ .

$\frac{v⃗}{| v⃗ |}$

Step 2

The norm is the square root of the sum of squares of each element in the vector.

$\sqrt{1^{2} + 3^{2}}$

Step 3

Simplify.

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Step 3.1

One to any power is one.

$\sqrt{1 + 3^{2}}$

Step 3.2

Raise $3$ to the power of $2$ .

$\sqrt{1 + 9}$

Step 3.3

Add $1$ and $9$ .

$\sqrt{10}$

Step 4

Divide the vector by its norm.

$\frac{(1, 3)}{\sqrt{10}}$

Step 5

Divide each element in the vector by $\sqrt{10}$ .

$(\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}})$

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