Linear Algebra Examples

$12 i - 9 j$

Step 1

The length of the vector is the square root of the quantity of the $i$ coordinate squared plus the $j$ coordinate squared.

$\sqrt{{(12)}^{2} + {(- 9)}^{2}}$

Step 2

Evaluate the square root.

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Step 2.1

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(- 9)}^{2}}$

Step 2.2

Raise $- 9$ to the power of $2$ .

$\sqrt{144 + 81}$

Step 2.3

Add $144$ and $81$ .

$\sqrt{225}$

Step 2.4

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

Step 2.5

Pull terms out from under the radical, assuming positive real numbers.

$15$

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