### All High School Math Resources

## Example Questions

### Example Question #1 : Calculus Ii — Integrals

The polar coordinates of a point are . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

**Possible Answers:**

**Correct answer:**

Given the polar coordinates , the -coordinate is . We can find this coordinate by substituting :

### Example Question #2 : Calculus Ii — Integrals

The polar coordinates of a point are . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

**Possible Answers:**

**Correct answer:**

Given the polar coordinates , the -coordinate is . We can find this coordinate by substituting :

### Example Question #1 : Calculus Ii — Integrals

The polar coordinates of a point are . Give its -coordinate in the rectangular coordinate system (nearest hundredth).

**Possible Answers:**

**Correct answer:**

Given the polar coordinates , the -coordinate is . We can find this coordinate by substituting :

### Example Question #1 : Parametric, Polar, And Vector

**Possible Answers:**

**Correct answer:**

Given the polar coordinates , the -coordinate is . We can find this coordinate by substituting :

### Example Question #1 : Vector

Find the vector where its initial point is and its terminal point is .

**Possible Answers:**

**Correct answer:**

We need to subtract the -coordinate and the -coordinates to solve for a vector when given its initial and terminal coordinates:

Initial pt:

Terminal pt:

Vector:

**Vector: **

### Example Question #6 : Calculus Ii — Integrals

Find the vector where its initial point is and its terminal point is .

**Possible Answers:**

**Correct answer:**

We need to subtract the -coordinate and the -coordinate to solve for a vector when given its initial and terminal coordinates:

Initial pt:

Terminal pt:

Vector:

**Vector: **

### Example Question #1 : Understanding Vector Calculations

Let be vectors. All of the following are defined EXCEPT:

**Possible Answers:**

**Correct answer:**

The cross product of two vectors (represented by "x") requires two vectors and results in another vector. By contrast, the dot product (represented by "") between two vectors requires two vectors and results in a scalar, not a vector.

If we were to evaluate , we would first have to evaluate , which would result in a scalar, because it is a dot product.

However, once we have a scalar value, we cannot calculate a cross product with another vector, because a cross product requires two vectors. For example, we cannot find the cross product between 4 and the vector <1, 2, 3>; the cross product is only defined for two vectors, not scalars.

The answer is .

### Example Question #2 : Understanding Vector Calculations

Find the magnitude of vector :

**Possible Answers:**

**Correct answer:**

To solve for the magnitude of a vector, we use the following formula:

### Example Question #1 : Understanding Vector Calculations

Given vector and , solve for .

**Possible Answers:**

**Correct answer:**

To solve for , we need to add the components in the vector and the components together:

### Example Question #4 : Understanding Vector Calculations

Given vector and , solve for .

**Possible Answers:**

**Correct answer:**

To solve for , we need to subtract the components in the vector and the components together: