# High School Math : Parametric, Polar, and Vector

## Example Questions

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### Example Question #1 : Understanding Polar Coordinates

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

Explanation:

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

### Example Question #1 : Understanding Polar Coordinates

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

Explanation:

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

### Example Question #3 : Understanding Polar Coordinates

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

Explanation:

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

### Example Question #1 : Polar

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

Explanation:

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 .

Explanation:

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 #2 : Vector

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

Explanation:

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:

Explanation:

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 :

Explanation:

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

### Example Question #3 : Understanding Vector Calculations

Given vector and , solve for .

Explanation:

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 .