Common Core: High School - Number and Quantity : Vector & Matrix Quantities

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

If , what is ?

Possible Answers:

Correct answer:

Explanation:

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 .

Screen shot 2016 03 07 at 3.54.13 pm

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

If , what is ?

Possible Answers:

Correct answer:

Explanation:

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 .

Screen shot 2016 03 07 at 3.59.16 pm

Example Question #81 : Vector & Matrix Quantities

If , what is ?

Possible Answers:

Correct answer:

Explanation:

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 .

Screen shot 2016 03 07 at 4.07.14 pm

Example Question #82 : Vector & Matrix Quantities

If , what is ?

Possible Answers:

Correct answer:

Explanation:

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 .

Screen shot 2016 03 07 at 4.20.14 pm

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 .

Explanation:

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.

Vecscale

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 .

 





Explanation:

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 

.Screen shot 2016 03 07 at 10.10.02 am

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 

Explanation:

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.

 


Screen shot 2016 03 07 at 10.16.42 am

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 .

Explanation:

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.


Screen shot 2016 03 07 at 10.20.27 am

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 .




 

Explanation:

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.


Screen shot 2016 03 07 at 10.32.32 am

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 .




Explanation:

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.

Screen shot 2016 03 07 at 10.42.39 am

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept
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