Question

Find the angle between the given vectors to the nearest tenth of a degree. u = <6, 4>, v = <7, 5>

Answer 1

Answer: 1.8°

Explanation:

To calculate the angle between the vectors u and v we use the formula of the dot product.

The dot product between two vecotores is:

`u\ *\ v = |u||v|*cosx`

Where x is the angle between the vectors

As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors

`u=6i + 4j\\v=7i +5j`

Then:

`u\ *\ v = 6*7 + 4*5`

`u\ *\ v = 42 + 20`

`u\ *\ v =62`

Now we calculate the magnitudes of both vectors

`|u|=√(6^2 + 4^2)\\\\|u|=2√(13)`

`|v|=√(7^2 +5^2)\\\\|v|=√(74)`

Then:

`62 = 2√(13)*√(74)*cosx`

Now we solve the equation for x

`62 = [tex]cosx=(62)/(2√(13)*√(74))\\\\x=arcos((62)/(2√(13)*√(74)))\\\\x=1.8\°`