# What is the angle between #<3 , -2 , 7 > # and # < 5, -3 , 2 > #?

##### 1 Answer

the angle is approximately 43.86 degrees

#### Explanation:

The formula for finding the angle between vectors is:

So first we need to find the dot product of the two vectors.

The dot product can be found simply adding up each corresponding element:

The magnitude can be found by square rooting the sum of the squares of the elements of a vector.

Magnitude of

Magnitude of

So now we have:

That, according to the calculator, equals to 43.86.

Alternatively, you can use the sine formula, which utilizes the cross product instead of the dot product, and it is slight more complicated.