Calculus 3 : Angle between Vectors

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #31 : Vectors And Vector Operations

Find the direction angles of the vector 

Possible Answers:

None of the Above

Correct answer:

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 =

Possible Answers:

None of the Above

Correct answer:

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.

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 .

Possible Answers:

None of the other answers

Correct answer:

None of the other answers

Explanation:

The correct answer is about  degrees.

 

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 .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

To find the angle, we use the formula .

So we have

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