# Scalar Multiples Worksheets

We use vectors to model force and motion. Both the value or magnitude and their direction are often provided or at least amble to be quantified through variously different means. Scalar can be applied to vectors and effect the values of these quantities. Scalars that are whole number that are greater than 1 increase the scale of the vector and those that are less than one either in fraction, decimal, or percentage form drawn down the scale. Below you will find a series of quality lessons and worksheets that show students how to find scalar multiples and their component values.

### Aligned Standard: HSN-VM.B.5b

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - I always like to start by find the value of the bisector and then proceed from there.
- Quiz 2 - It may help you to redraw the angles for yourself.
- Quiz 3 - It is helpful that everything is a perfect bisector here.

### 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. For instance, if you were given a vector (v) and knew it’s position as (-3,2) and you wanted to know how it interacted with the scalar 4, you would solve it as: 4v which would than require the math:

4v = 4(-3, 2)

= ((4)-3, (4)2)

= -12, 8