### All Calculus 3 Resources

## Example Questions

### Example Question #11 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are not orthogonal.

The two vectors are orthogonal.

**Correct answer:**

The two vectors are orthogonal.

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.

### Example Question #12 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are not orthogonal.

**Correct answer:**

The two vectors are orthogonal.

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.

### Example Question #13 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are not orthogonal.

**Correct answer:**

The two vectors are not orthogonal.

Vectors can be said to be orthogonal, that is to say perpendicular or normal, if their dot product amounts to zero:

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are not orthogonal.

### Example Question #14 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are not orthogonal.

**Correct answer:**

The two vectors are orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.

### Example Question #15 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are *not* orthogonal.

**Correct answer:**

The two vectors are orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.

### Example Question #16 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are not orthogonal.

The two vectors are orthogonal.

**Correct answer:**

The two vectors are not orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are not orthogonal.

### Example Question #17 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are not orthogonal.

The two vectors are orthogonal.

**Correct answer:**

The two vectors are not orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are not orthogonal.

### Example Question #18 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are not orthogonal.

**Correct answer:**

The two vectors are orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.

### Example Question #19 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are not orthogonal.

The two vectors are orthogonal.

**Correct answer:**

The two vectors are not orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are not orthogonal.

### Example Question #20 : Normal Vectors

Determine whether the two vectors, and , are orthogonal or not.

**Possible Answers:**

The two vectors are orthogonal.

The two vectors are *not* orthogonal.

**Correct answer:**

The two vectors are orthogonal.

To find the dot product of two vectors given the notation

Simply multiply terms across rows:

For our vectors, and

The two vectors are orthogonal.