2D Vectors

A vector always has . . .

• A tail

• A head

• A direction

• A magnitude

Answer explanation

A vector always has a tail, head, direction, and magnitude.

Well, almost. There is one exception to this rule: The so-called "zero vector." You should read more about vectors and the zero vector by clicking on this link: https://mathinsight.org/zero_vector

Tags

CCSS.HSN.VM.A.1

A 2D vector is always at an angle to the horizontal axis. Which symbol is used to represent this angle?

Answer explanation

A 2D vector is always at an angle to the horizontal axis. The symbol used to represent this angle is the Greek lowercase letter theta (θ).

If you want to hear how a robot pronounces the symbol theta, you can listen to this video: https://youtu.be/Os9Szmf3dZs

Tags

CCSS.HSF.TF.A.3

CCSS.HSG.CO.A.1

CCSS.HSG.CO.C.9

A student draws a 2D vector and gives it the symbol d with a half-arrow above it. How would the student properly notate the magnitude of this vector?

• 
• 
• 
• 

Answer explanation

The magnitude of a vector is notated by writing the vector's symbol inside of the absolute value bars | |.

Remember: The magnitude of a vector is just another word for the vector's size, or length.

Tags

CCSS.HSN.VM.A.1

Look at the given 2D vector. What is its angle (θ)?

Answer explanation

The angle of this 2D vector is 0 degrees. This means that the vector is directedly solely along the x-axis and in the positive direction of the x-axis.

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.A.2

Look at the given 2D vector. What is its angle (θ)?

Answer explanation

The angle of this 2D vector is 90 degrees. This means that the vector is directedly solely along the y-axis and in the positive direction of the y-axis.

Tags

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.C.6

CCSS.HSF.TF.A.3

CCSS.HSG.SRT.D.11

Look at the given 2D vector. What is its angle (θ)?

Answer explanation

The angle of this 2D vector is 180 degrees. This means that the vector is directedly solely along the x-axis and in the negative direction of the x-axis.

Tags

CCSS.HSN.VM.A.1

Consider the vector a = <3, 4>. What is the magnitude of this vector?

• 5

• 3

• 4

• 7

Answer explanation

Use the Pythagorean Theorem to solve this problem. Refer back to the notes if you need help.

Tags

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.C.6

Consider the vector b = <5, 12>. What is the magnitude of this vector?

• 5

• 17

• 12

• 13

Answer explanation

Use the Pythagorean Theorem to solve this problem. Refer back to the notes if you need help.

Tags

CCSS.HSN.VM.A.2

CCSS.HSN.VM.A.3

Consider the vector c = <20, 21>. What is the magnitude of this vector?

• 20

• 21

• 29

• 41

Answer explanation

Use the Pythagorean Theorem to solve this problem. Refer back to the notes if you need help.

Consider the vector d = <5, 5>. What is the angle of this vector?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

Answer explanation

Make sure to use the arctan() function to solve this problem. Refer back to the notes if you need to.

Tags

CCSS.HSG.SRT.C.8

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.D.11