Home > Grade Levels > High School Numbers and Quantity >

Magnitudes of Scalar Multiples

Answer Keys Here

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 =[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.