Calculus 3 : Angle between Vectors

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #11 : Vectors And Vector Operations

Find the angle between the two vectors. 

Possible Answers:

No angle exists

Correct answer:

Explanation:

To find the angle between two vector we use the following formula

and solve for .

Given

we find

Plugging these values in we get

To find  we calculate the  of both sides

and find that

Example Question #12 : Vectors And Vector Operations

Find the approximate angle in degrees between the vectors .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

We can compute the (acute) angle between the two vectors using the formula

Hence we have

Example Question #13 : 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 approximately  degrees.

 

To find the angle between two vectors, we use the equation .

Hence we have 

(This answer is small due to the fact that the two vectors nearly point in the same direction, due to  and  being close in value.)

Example Question #14 : Vectors And Vector Operations

Find the acute angle in degrees between the vectors .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To find the angle between two vectors, we use the formula

.

So we have

Example Question #15 : Vectors And Vector Operations

Find the angle between the following vectors (to two decimal places):

Possible Answers:

0.98

1.18

1.46

2.89

1.62

Correct answer:

1.46

Explanation:

The dot product is defined as:

Where theta is the angle between the two vectors.  Solving for theta:

To solve each component:

Putting it all together, we can solve for theta:

Example Question #16 : Vectors And Vector Operations

Find the angle between vectors  and  and round to the nearest degree.

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the angle between two vectors.

Evaluate each term.

Substitute the values into the equation.

The correct answer is:  

Example Question #17 : Vectors And Vector Operations

Find the angle between the two vectors

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 #18 : Vectors And Vector Operations

What is the angle to the nearest degree between the vectors  and ?

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 #19 : Vectors And Vector Operations

Find the angle between the two vectors

and

Round to the nearest degree.

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 #20 : Vectors And Vector Operations

Find the angle between the two vectors

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

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