# Calculus 3 : Angle between Vectors

## Example Questions

### Example Question #31 : Vectors And Vector Operations

Find the direction angles of the vector

None of the Above

Explanation:

To find the direction angles we must first find the Unit vector of

Then we use Cosine to find each angle:

so,

### Example Question #32 : Vectors And Vector Operations

If a = (3,2,1) and b = (6,α,2) are parallel, then α =

None of the Above

Explanation:

If a and b are parallel, then there is a scaler multiple of :

in this case . Therefore,

so,

### Example Question #33 : Vectors And Vector Operations

Find the angle between the vectors

Round to the nearest tenth.

Explanation:

### In order to find the angle between the two vectors, we follow the formula

and solve for

Using the vectors in the problem, we get

Simplifying we get

To solve for

we find the

of both sides and get

and find that

### Example Question #34 : Vectors And Vector Operations

Find the angle between the vectors  and , given that , and

Explanation:

Using the dot product formula . Plugging in what we were given in the problem statement, we get . Solving for  we get .

### Example Question #35 : Vectors And Vector Operations

Find the angle between the vectors  and , given that , and

Explanation:

Using the dot product formula . Plugging in what we were given in the problem statement, we get . Solving for  we get .

### Example Question #36 : Vectors And Vector Operations

Find the angle between the vectors  and  if  and . Hint: Do the dot product between the vectors to start.

Explanation:

First, you must do the dot product of the vectors, because the answer choices are in terms of inverse cosine. Doing the dot product gets . Next, you must find the magnitude of both vectors.  and . Combining everything we have found and using the formula for the dot product, we get . Solving for , we then get .

### Example Question #37 : Vectors And Vector Operations

Find the angle between the vectors  and , given that .

Explanation:

To find the angle between the vectors, we use the formula for the dot product:

. Using this definition, we find that . Putting what we know into the formula, we get . Solving for theta, we get

### Example Question #38 : Vectors And Vector Operations

Find the angle between the vectors  and , given that .

Explanation:

To find the angle between the vectors, we use the formula for the cross product:

. Using this definition, we find that . Putting what we know into the formula, we get . Solving for theta, we get

### Example Question #39 : Vectors And Vector Operations

Find the angle in degrees between the vectors .

None of the other answers

None of the other answers

Explanation:

To find the angle, we use the formula .

So we have

### Example Question #40 : Vectors And Vector Operations

Find the angle in degrees between the vectors .