Multiplication of Vectors

# Multiplication of Vectors

GCSE(F), GCSE(H),

Vectors can be multiplied.

a + a + a = 3a

The multiplier of the vector is called a scalar. A scalar can take any numeric value, including negative values.

In the example above, c = 3b. Similarly, a = frac(1)(2)d.

## Examples

1. State the resultant vector vec(AB) in terms of a and b.

Answer: 4bb(a) + 3bb(b)

Four instances of a along; and three instances of b up.

2. What is the magnitude of 2bb(a) + 3bb(b), if bb(a)=((3),(2)) and bb(b)=((2),(-3))?

2bb(a) + 3bb(b) = 2((3),(2)) + 3((2),(-3)) = ((6),(4)) + ((6),(-9)) = ((12),(-5))
The magnitude of the vector = sqrt(12^2 + -5^2) = 13