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Multiplication of Vectors

Multiplication of Vectors

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 amd fractional values.

Multiplication of Vectors

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

Example 1

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

What multiple of vectors is required to get to a point?

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

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

Example 2

State the resultant vector `vec(CD)` in terms of e and f.

Multipliction of vectors with fraction and negative scalars

To get from C, move `1frac(1)(2)` worth of e in the opposite direction; and 1 worth of f in the opposite direction.

Answer: -1.5e - f