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## Magnitudes of Scalar Multiples

#### 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 =[kvx1,kvx2 .. kvxn] 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  #### 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.