Scalar Multiplication, Magnitude, & Direction (Grades 11-12)
Print Test
(Only the test content will print)
Name: | Date: |
---|
Scalar Multiplication, Magnitude, & Direction
Instructions: Unless otherwise stated, the direction of a vector is considered to be the angle between the positive x-axis and the vector (with its tail at the origin), going from the positive x-axis to the vector in a counterclockwise direction.
1.
For [math]vec{v} = <<-4,2>>[/math], find [math]||3vec{v}||[/math].
- [math]6[/math]
- [math]2sqrt(5)[/math]
- [math]6sqrt(5)[/math]
- [math]60[/math]
2.
If [math]||5vec{u}|| = 15[/math], what is the value of [math]||vec{u}|| ?[/math]
- 3
- 5
- 10
- Not enough information to determine.
3.
If the direction of [math]vec{v}[/math] is 60°, what is the direction of [math]-3vec{v}[/math]?
- 240°
- -180°
- 60°
- 180°
4.
For vectors [math]vec{n} = 6vec{v}[/math] and [math]vec{m} = -12vec{v}[/math], which of the following statements are correct? Choose all correct answers.
- The vectors have opposite directions.
- [math]-2||vec{n}|| = ||vec{m}||[/math]
- Both vectors are in the same direction as [math]vec{v}[/math].
- The magnitude of [math]vec{m}[/math] is twice that of [math]vec{n}[/math].
5.
For [math]vec{v} = <<0,4>>[/math], find the direction of [math]3vec{v}[/math].
- 270°
- 180°
- 90°
- 0°
6.
For [math]vec{v} = <<3,2>>[/math], find [math]|| -10vec{v}||[/math].
- [math] -10sqrt{13}[/math]
- [math]sqrt{130}[/math]
- [math]50[/math]
- [math]10sqrt{13}[/math]
7.
If you are given [math]vec{v}[/math], which of the following is a vector that is twice as long but in the opposite direction?
- [math]2vec{v}[/math]
- [math]-2vec{v}[/math]
- [math]1/2 vec{v}[/math]
- [math]-1/2 vec{v}[/math]
8.
For a given vector, [math]vec{v}[/math], and scalar multiple [math]a, \ a<0[/math], which of the following statements is correct?
- The direction of [math]a \ vec{v}[/math] is the same as the direction of [math]vec{v}[/math].
- The direction of [math]a \ vec{v}[/math] is opposite to that of [math]vec{v}[/math].
- The direction of the two vectors is different, but it is impossible to tell how they are different.
- The direction of the two vectors is different, but the difference will be less than 180°.
9.
Which of the following statements is true if [math]vec{v}[/math] is a non-zero vector, [math]a[/math] is a scalar such that [math]a< -1[/math], and [math]vec{w} = a vec{v} ?[/math]
- [math]||vec{w}|| = ||a vec{v}||[/math]
- [math]||vec{w}|| < ||a vec{v} || [/math]
- [math]||vec{w}|| > ||a vec{v} || [/math]
- [math] || vec{w}|| = - || vec{v}||[/math]
10.
For the vectors [math]vec{n}[/math] and [math]vec{m}[/math], [math]||a \ vec{n}|| = ||vec{m}||[/math] for scalar [math]a[/math], where [math]a[/math] can be any non-zero real number. Which of the following statements must be true?
- The two vectors have the same direction.
- The two vectors have the opposite direction.
- The ratio of the magnitudes of [math]vec{m}[/math] to [math]vec{n}[/math] is [math]a[/math] to [math]1[/math].
- The two vectors are equal.
You need to be a HelpTeaching.com member to access free printables.
Already a member? Log in for access. | Go Back To Previous Page
Already a member? Log in for access. | Go Back To Previous Page