## Magnitudes of Scalar Multiples

#### Aligned To Common Core Standard:

**High School** - HSN-VM.B.5b

What are Magnitudes of Scalar Multiples?
The concept of vectors is essential, given its extensive usage in physics and mathematical physics. Scalar quantity is something that doesn't have a direction such as the length of a curtain. While vector has a direction such as gravity. Magnitude is the quantity aspect of a vector. In other words, if we combine magnitude of a vector and the quantity of scalar, they are the same.
Let us multiply a scalar k with vector v: We will simply multiply k with every component of the vector. Let us solve the problem in a vector form.
kv =[kvx_{1},kvx_{2} .. kvx_{n}]
All the components get multiplied by the scalar value, and the combination becomes the resultant magnitude of the vector.
A series of quality lessons and worksheets that show students how to find scalar multiples and their component values.

### Printable Worksheets And Lessons

- Missing Vector Angles Step-by-step Lesson- A quick way to find all the angles between two simple vectors.

- Guided Lesson - Find all the products of two vectors.

- Guided Lesson Explanation - The absolute value is important in these problem forms. Make sure to point that out to students.

- Practice Worksheet - Three pages of problems for you to get the hang of this skill.

- Matching Worksheet - This is quite a little feat if they can pull it off in under 10 minutes.

- Translations And Vectors Geo Worksheet Five Pack- See if you can follow the graphs. Some people have to trace the steps.

#### Homework Sheets

This skill transfers right into vectors.

- Homework 1 - The angle between a and b must be 90° as the angle between i and j planes is always 90°.
- Homework 2 - Angle between vectors b and c and a and c must be 20° as the angle between the vectors a and b is 40° because vector c is bisecting the vectors a and b.
- Homework 3 - If you would like to solve these easily, just break it down into pieces.

#### Practice Worksheets

It's funny how many everyday applications geometry has in physics. I call it "Physics Math"!

- Practice 1 - If a = 9i, b = 2j and c = i+j, the angle between a and b is 90°, and it is given that c bisects a and b, find: (a) a.b, (b) a.c, (c) b.c
- Practice 2 - Remember that a bisector cuts an angle into two equal parts of half.
- Practice 3 - We take this math for granted, but air traffic controllers would have an even tougher job if computers couldn't crunch data and apply this for them.

#### Math Skill Quizzes

It looks like 4 questions, but it is really 12 questions per quiz.