Linear Algebra Examples

$7 j - i$

Step 1

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

$\sqrt{{(- 1)}^{2} + {(7)}^{2}}$

Step 2

Evaluate the square root.

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Step 2.1

Raise $- 1$ to the power of $2$ .

$\sqrt{1 + {(7)}^{2}}$

Step 2.2

Raise $7$ to the power of $2$ .

$\sqrt{1 + 49}$

Step 2.3

Add $1$ and $49$ .

$\sqrt{50}$

Step 2.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.4.1

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Step 2.4.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2}$

Step 2.5

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$