## Vector Sums Magnitude and Direction

#### Aligned To Common Core Standard:

**High School** - HSN-VM.B.4b

How to Find Vector Sums of Magnitude and Direction - Mathematical operations on vectors are usually common when you are learning advanced mathematics. One of the basic mathematical operations used in Vectors is Vector addition. You can add two vectors to determine the resultant (or result) of the two vectors. However, it is important to understand that direction plays an important part in finding out the result of adding two vectors. Let us consider an example, and if you are moving a box of books horizontally, then the applied force is in the direction parallel to the x-axis. However, if you apply the force from upwards, the direction is downwards and the box stays at the same place. Let us take an example. Thomas and Clark play soccer for two different teams in the school. During an exhibition match, they came head to head and kicked the ball simultaneously in the opposite direction. Thomas kicked the ball with a force of 66N, while Clark kicked it with a force of 70N. Find out the net force of the ball. Now, there are two forces acting on the ball. Thomas standing at one end applies a force of 66N on it, while the strong Clark kicked it back with 70N. That means Thomas' kick canceled out the force of Clark's kick. The force of Thomas and Clark's kicks are denoted by T and C respectively. Resultant = C + T: Due to the opposite direction of the forces, the resultant will consist of vector subtraction. Resultant=C+(-T) | Resultant=70-66 | Resultant=4N. The direction of the force is Clark's kick due to its increased value. These worksheets and lessons show you how to find sums between vectors in the way of both magnitude and direction.

### Printable Worksheets And Lessons

- Visualizing Vector Sums Step-by-step Lesson- I give you a word problem that will prompt you to draw the vectors first.

- Guided Lesson
- This is where you might start to lose some students. Make sure that they understand every step along the way.

- Guided Lesson Explanation - I tried to make this very clear. I might have added an extra step or two.

- Practice Worksheet - This one can be very time consuming. It took one of my students just under an hour to complete it.

- Matching Worksheet - Match the vector word problem to its outcome.

#### Homework Sheets

For this skill we compound two calculations to get a better understanding of the vector.

- Homework 1 - Find the supplementary angle to find an angle of the triangle.
- Homework 2 - Use the Law of cosines to find the direction.
- Homework 3 - Find the measurement of the angle between the vector of the 15 pounds and the vector of the 20 pounds force to the nearest whole degree.

#### Practice Worksheets

We now translate this skill to real world word problems.

- Practice 1 - Two forces with magnitudes of 21 pounds and 23 pounds are applied to the same fixed object. The magnitude of the resultant force is 10 pounds. Find the measurement of the angle between the resultant vector and the vector of the 21 pounds force to the nearest whole degree.
- Practice 2 - A vector u has a magnitude of 10 and a direction of 0°. A vector v has a magnitude of 20 and a direction of 30°. Find the direction and magnitude of u +v to the nearest whole values.
- Practice 3 - Round to the nearest whole degree as needed.

#### Math Skill Quizzes

Make sure to review the use of angles in these. The angle 0° seems to give kids trouble and trips them up.