## Vector Direction - Exercise

The Vector Direction Concept Builder is comprised of 54 questions. The questions are divided into 18 different question groups with three questions in each group. Questions in the same group are similar to one another; they may include three different vectors located in the same quadrant or three different vectors, each being 15° from an axis. The Concept Builder is coded to select at random a question from each group until a student is successful with that group of questions.

There are three activities which a student can do in this Concept Builder. Those activities are differentiated as follows:

• Counter-Clockwise from East: Question Groups 1-6; students are given a diagram of a vector and drag a protractor into position in order to measure an angle and express the direction of the vector as a counter-clockwise angle of rotation from due east.
• Rotation Angle from Nearest Axes: Question Groups 7-12; students are given a diagram of a vector and drag a protractor into position in order to measure an angle and express the direction of the vector as the angle of rotation from one of the two nearest axes.
• Convention Conversions: QuestionGroups 13-18; students are given the direction of a vector in one of the two conventions and must do some spatial/mathematical reasoning in order to express the directoin in the other convention.

The questions from each group are shown below. Teachers are encouraged to view the questions in order to judge which activity or activities are most appropriate for their classes.

The Physics Classroom grants teachers and other users the right to print these questions for private use. Users are also granted the right to copy the text and modify it for their own use. However, this document should not be uploaded to other servers for distribution to and/or display by others. The Physics Classroom website should remain the only website or server from which the document is distributed or displayed. We also provide a PDF that teachers can use under the same conditions. We have included a link to the PDF near the bottom of this page.

Question Group #1
Questions 1 - 3
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #2
Questions 4 - 6
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #3
Questions 7 - 9
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #4
Questions 10 - 12
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #5
Questions 13 - 15
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #6
Questions 16 - 18
Use the protractor to determine the direction of the given vector. Express your answer using the counter-clockwise (CCW) from East convention. (The angle measure is a multiple of 15 degrees.)

Question Group #7
Questions 19 - 21
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #8
Questions 22 - 24
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #9
Questions 25 - 27
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #10
Questions 28 - 30
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #11
Questions 31 - 33
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #12
Questions 34 - 36
Use the protractor to determine the direction of the given vector. Express your answer as an angle of rotation some direction from one of the two nearest axes. (The angle measure is a multiple of 15 degrees.)

Question Group #13
Question 37
Perform the following convention conversion for the given direction.

Convert 117° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 38
Perform the following convention conversion for the given direction.

Convert 129° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 39
Perform the following convention conversion for the given direction.

Convert 158° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question Group #14
Question 40
Perform the following convention conversion for the given direction.

Convert 199° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 41
Perform the following convention conversion for the given direction.

Convert 214° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 42
Perform the following convention conversion for the given direction.

Convert 257° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question Group #15
Question 43
Perform the following convention conversion for the given direction.

Convert 299° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 44
Perform the following convention conversion for the given direction.

Convert 312° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question 45
Perform the following convention conversion for the given direction.

Convert 348° counter-clockwise from east to an angle of rotation from one of the two nearest axes.

Question Group #16
Question 46
Perform the following convention conversion for the given direction.

Convert 74° N of W to the counter-clockwise from east convention.

Question 47
Perform the following convention conversion for the given direction.

Convert 49° N of W to the counter-clockwise from east convention.

Question 48
Perform the following convention conversion for the given direction.

Convert 7° N of W to the counter-clockwise from east convention.

Question Group #17
Question 49
Perform the following convention conversion for the given direction.

Convert 21° S of W to the counter-clockwise from east convention.

Question 50
Perform the following convention conversion for the given direction.

Convert 37° S of W to the counter-clockwise from east convention.

Question 51
Perform the following convention conversion for the given direction.

Convert 73° S of W to the counter-clockwise from east convention.

Question Group #18
Question 52
Perform the following convention conversion for the given direction.

Convert 67° S of E to the counter-clockwise from east convention.

Question 53
Perform the following convention conversion for the given direction.

Convert 52° S of E to the counter-clockwise from east convention.

Question 54
Perform the following convention conversion for the given direction.

Convert 24° S of E to the counter-clockwise from east convention.