Find a.b if |a| = 3, |b| = 14, and the angle between a and b is 45°.

Solution:

Given are the magnitude of the two vectors a and b and the angle formed between them.

We know that dot product a . b = |a| |b| cos θ

Given: |a| = 3, |b| = 14 and the angle between a and b, θ = 45°

Dot product a . b = |a| × |b| × cos θ

= 3 × 14 × cos45°

= 42/√2

= 42/√2 × √2/√2

=(42√2)/2

=21√2

a.b =21√2

Find a.b if |a| = 3, |b| = 14, and the angle between a and b is 45°.

Summary:

If |a| = 3, |b| = 14 and the angle between a and b is 45°, then the value of a . b =21√2