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

## Example Questions

### Example Question #9 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If , what is ?

**Possible Answers:**

**Correct answer:**

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

where is the scalar.

In this case it is

The final answer is then .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

### Example Question #10 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If , what is ?

**Possible Answers:**

**Correct answer:**

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

where is the scalar.

In this case it is

The final answer is then .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

### Example Question #81 : Vector & Matrix Quantities

If , what is ?

**Possible Answers:**

**Correct answer:**

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

where is the scalar.

In this case it is

The final answer is then .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

### Example Question #82 : Vector & Matrix Quantities

If , what is ?

**Possible Answers:**

**Correct answer:**

where is the scalar.

In this case it is

The final answer is then .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

### Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is away from .

, Direction is away from .

, Direction is away from .

, Direction is the same as .

, Direction is the same as .

**Correct answer:**

, Direction is away from .

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

, where is a scalar.

Now lets calculate this.

As for the direction of the vector, since , the resulting vector will be against the original vector .

See below for a picture.

### Example Question #2 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is the same as .

, Direction is the same as .

, Direction is away from .

, Direction is the same as .

, Direction is away from .

**Correct answer:**

, Direction is the same as .

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

, where is a scalar.

Now lets calculate this.

As for the direction of the vector, since , the resulting vector will be in the same direction as the original vector

.

### Example Question #1 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is the same as .

, Direction is away from .

, Direction is the same as

, Direction is the same as .

, Direction is away from .

**Correct answer:**

, Direction is the same as

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

, where is a scalar.

Now lets calculate this.

As for the direction of the vector, since , the resulting vector will be in the same direction as the original vector .

See below for a picture.

### Example Question #4 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is away from .

, Direction is away from .

, Direction is away from .

, Direction is the same as .

, Direction is the same as .

**Correct answer:**

, Direction is away from .

, where is a scalar.

Now lets calculate this.

As for the direction of the vector, since , the resulting vector will be against the original vector .

See below for a picture.

### Example Question #5 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is the same as .

, Direction is away from .

, Direction is away from .

, Direction is the same as .

, Direction is away from .

**Correct answer:**

, Direction is away from .

, where is a scalar.

Now lets calculate this.

As for the direction of the vector, since , the resulting vector will be against the original vector .

See below for a picture.

### Example Question #6 : Compute Magnitude And Direction Of A Scalar Multiple: Ccss.Math.Content.Hsn Vm.B.5b

Calculate , where . Also determine the direction of the resulting vector.

**Possible Answers:**

, Direction is away from .

, Direction is the same as .

, Direction is the same as .

, Direction is away from .

, Direction is away from .

**Correct answer:**

, Direction is away from .

, where is a scalar.

Now lets calculate this.

See below for a picture.