The dot product of two vectors: for A Level Further Maths

 

The dot product or scaler product of two vectors, a and b, is defined as follows:

a.b = |a| |b| cos θ

Since |a|, |b| and cos t are scalers, the dot product is a scaler.

The dot product of unit vectors

i.i = |i| |i| cos 0 = 1 X 1 X 1 = 1

i.j = |i| |j| cos 90 = 1 X 1 X 0 = 0

j.j = |j| |j| cos 0 = 1 X 1 X 1 = 1

The dot product of two perpendicular vectors is zero.

E.g.

a = 3i + 4j   b = 5i - 12j  θ = 60

|a| = 5   |b| = 13

a.b = |a| |b| cos θ

a.b = 5 X13 X cos 60

a.b = 32.5

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