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

## Example Questions

### 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 the same as .

, Direction is the same as .

, Direction is away from .

, Direction is away from .

**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 #3 : 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 away from .

, Direction is the same as .

**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 the same as .

, Direction is away from .

, Direction is away from .

, 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 the same as .

, Direction is away from .

, Direction is away from .

, 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 away from .

, Direction is the same as .

, Direction is the same as .

, Direction is away from .

**Correct answer:**

, Direction is away from .

, where is a scalar.

Now lets calculate this.

See below for a picture.

### Example Question #7 : 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 away from .

, Direction is the same as .

**Correct answer:**

, Direction is the same as .

, where is a scalar.

Now lets calculate this.

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

See below for a picture.

### Example Question #8 : 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 away from .

, Direction is away from .

**Correct answer:**

, Direction is the same as .

, 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 #9 : 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 away from .

, Direction is away from .

, Direction is the same as .

**Correct answer:**

, Direction is the same as .

, 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 #10 : 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 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.

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