### All Common Core: High School - Number and Quantity Resources

## Example Questions

### Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

**Possible Answers:**

**Correct answer:**

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

Now lets identify what these values are.

To write this in component form, we need to put our , and into .

So the final answer is

Below is a visual representation of what we just did.

### Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

**Possible Answers:**

**Correct answer:**

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

Now lets identify what these values are.

To write this in component form, we need to put our , and into .

So the final answer is

Below is a visual representation of what we just did.

### Example Question #11 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

**Possible Answers:**

**Correct answer:**

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

Now lets identify what these values are.

To write this in component form, we need to put our , and into .

So the final answer is

Below is a visual representation of what we just did.

### Example Question #12 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of , and an initial point of ?

**Possible Answers:**

**Correct answer:**

Now lets identify what these values are.

To write this in component form, we need to put our , and into .

So the final answer is

Below is a visual representation of what we just did.

### Example Question #1 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Bob is cruising south down a river at , and the river has current due west. What is Bob's actual speed?

**Possible Answers:**

Not possible to find

**Correct answer:**

In order to figure this out, we need to create a picture.

Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Bob is actually going.

Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.

For our calculations, let , and .

### Example Question #2 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Amanda is cruising north down a river at , and the river has current due east. What is Amanda's actual speed?

**Possible Answers:**

**Correct answer:**

In order to figure this out, we need to create a picture.

Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Amanda is actually going.

Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.

For our calculations, let , and .

### Example Question #3 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Jack slides down a hill at , and throws a rock behind him at . How fast is the rock going?

**Possible Answers:**

**Correct answer:**

Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill.

### Example Question #3 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

If an airplane is flying south at , and there are winds coming from the west at , how fast is the plane going?

**Possible Answers:**

**Correct answer:**

In order to figure this out, we need to create a picture.

Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed the airplane is actually going.

Recall that the Pythagorean Theorem is , where is the hypotenuse, and , are the legs of the triangle, and have a angle between them.

For our calculations, let , and .

### Example Question #2 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Jill slides down a hill at , and throws a coin forward at . How fast is the coin going?

**Possible Answers:**

**Correct answer:**

Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill.

### Example Question #4 : Vector Representation Of Quantities (Velocity, Etc.): Ccss.Math.Content.Hsn Vm.A.3

Bob slides down a hill at , and throws his wallet behind him at . How fast is his wallet going?

**Possible Answers:**

**Correct answer:**

Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill.

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