To add two vectors, add their coordinates or components.

Given = (2, 1, 3), = (1, −1, 0) and = (1, 2, 3), find the vector = 2u + 3v − w.

= (4, 2, 6) + (3, −3, 0) − (1, 2, 3) = (6, −3, 3)

Given vectors and , determine the magnitude of the vector .

Properties of Vector Addition

Associative.

+ ( + ) = ( + ) +

Commutative.

+ = +

Additive identity.

+ =

Additive inverse or opposite.

+ (− ) =

Scalar Multiplication

The product of a number k by a vector is another vector:

In the same direction as if k is positive.

In opposite direction as if k is negative.

Of magintude .

Superprof

Properties

Associative.

k · (k' · ) = (k · k') ·

Right distributivity.

k · ( + ) = k · + k ·

Left distributivity.

(k + k') · = k · + k' ·

Multiplicative Identity.

1 · =

Example

Given = (6, 2, 0), determine so that 3 = .

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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