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Examples

(12, - 5) \cdot (5, 6)

$(12, - 5) \cdot (5, 6)$

Step 1

The dot product of two vectors is the sum of the products of the their components.

12 \cdot 5 - 5 \cdot 6

$12 \cdot 5 - 5 \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

12

$12$ by

5

$5$ .

60 - 5 \cdot 6

$60 - 5 \cdot 6$

Step 2.1.2

Multiply

- 5

$- 5$ by

6

$6$ .

60 - 30

$60 - 30$

60 - 30

$60 - 30$

Step 2.2

Subtract

30

$30$ from

60

$60$ .

30

$30$

30

$30$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$