Question

Determine the angle measure between vectors u and v: u = – 3i + 3j and v = 3i + 2j .

Answer 1

`\theta=101.3\degree` to the nearest tenth

Explanation:

The given vectors are;

u = – 3i + 3j and v = 3i + 2j

We use the dot product to find the angle between the two vectors.

`u\bullet v=|u| |v|\cos \theta`

`(-3i+3j)\bullet (3i+2j)=|-3i+3j| |3i+3j|\cos \theta`

`(-3i+3j)\bullet (3i+2j)=√((-3)^2+3^2) √(3^2+2^2)\cos \theta`

`-9+6=3√(2) √(13)\cos \theta`

`-3=3√(2) √(13)\cos \theta`

`-1=√(26) \cos \theta`

`-(1)/(√(26))= \cos \theta`

`\cos^(-1)(-(1)/(√(26)))= \theta`

`\theta=101.3\degree`