Question

Find the angle between u = (8.- 3) and v = (-3,- 8) Round to the nearest tenth of a degree.

a. 180
c. 0
b. 90
d. 450

Answer 1

B

Explanation:

edge answer

Answer 2

90°

Explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

`|u|=√((8)^2 + (-3)^2) \\\\|u|=√(64 + 9)\\\\|u|=8.544`

The module of v is:

`|v|=√((-3)^2 + (-8)^2) \\\\|u|=√(9 + 64)\\\\|u|=8.544`

Now we calculate the scalar product between both vectors

`u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0`

Finally we know that the scalar product of two vectors is equal to:

`u*v = |u||v|*cos(\theta)`

Where
`\theta` is the angle between the vectors u and v. Now we solve the equation for
`\theta`

`0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°`

the answer is 90°

Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °