Vector Addition

To add two vectors, add their coordinates or components.

Vectors

Vector Addition

Examples

Given Vector U= (2, 1, 3), Vector V = (1, −1, 0) and Vector W = (1, 2, 3), find the vector Vector X = 2u + 3v − w.

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

Given vectors Vector U and Vector V, determine the magnitude of the vector Vector Subtraction.

Vector Subtraction

Vector Subtraction

Properties of Vector Addition

Associative.

Vector U + (Vector V + Vector W ) = (Vector U + Vector V) + Vector W

Commutative.

Vector + Vector = Vector +

Additive identity.

Vector + Vector =

Additive inverse or opposite.

Vector + (− Vector) = Vector


Scalar Multiplication

The product of a number k Set Membership Real Number by a vector Vector is another vector:

In the same direction as Vector if k is positive.

In opposite direction as Vector if k is negative.

Of magintude Vector Magnitude.

Vector Product


Properties

Associative.

k · (k' · u ) = (k · k') ·

Right distributivity.

k · ( u + v ) = k · u + k ·

Left distributivity.

(k + k') · u = k · u + k' ·

Multiplicative Identity.

1 · u =


Example

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

Vector Calculations