Linear Algebra Examples

(1, - 1, 2) \cdot (5, 2, 4)

$(1, - 1, 2) \cdot (5, 2, 4)$

Step 1

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

1 \cdot 5 - 1 \cdot 2 + 2 \cdot 4

$1 \cdot 5 - 1 \cdot 2 + 2 \cdot 4$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply

5

$5$ by

1

$1$ .

5 - 1 \cdot 2 + 2 \cdot 4

$5 - 1 \cdot 2 + 2 \cdot 4$

Step 2.1.2

Multiply

- 1

$- 1$ by

2

$2$ .

5 - 2 + 2 \cdot 4

$5 - 2 + 2 \cdot 4$

Step 2.1.3

Multiply

2

$2$ by

4

$4$ .

5 - 2 + 8

$5 - 2 + 8$

5 - 2 + 8

$5 - 2 + 8$

Step 2.2

Subtract

2

$2$ from

5

$5$ .

3 + 8

$3 + 8$

Step 2.3

Add

3

$3$ and

8

$8$ .

11

$11$

11

$11$

Enter YOUR Problem