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Multiply a Vector by a Scalar

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Aligned To Common Core Standard:

High School - HSN-VM.B.5

How to Multiply a Vector by a Scalar - Vectors and algebra are quite alike, given that the coefficient changes the value of the unknown variable in algebra. While scale quantity increases the value (magnitude in vectors). Multiplying a vector with a scalar increases the magnitude however, the direction of the vector remains the same. Let us take a few examples of multiplying a vector with a scalar quantity. Suppose you have a vector 2i+3j-5k, and you have to multiply the vector with the scalar 5. 5 (2i+3j-5k) | 10i+15j-25k) | It's quite simple, you just have to multiply the constant number or scalar quantity with the vector quantity. Geometrically, you can say that the length of the vector increases in all the dimensions. These worksheets focus on understanding and using the components of a vector. The lessons show you how to add scale to that vector.

Printable Worksheets And Lessons

Homework Sheets

Find angles, vectors, and magnitudes of vectors.

  • Homework 1 - When we find the dot product of given vectors, it tells us that: A * B = Ax Bx + Ay By+ Az Bz
  • Homework 2 - A perpendicular vector can be found by finding the cross product of both vectors.
  • Homework 3 - Taking inverse on both sides will give the value of Θ .

Practice Worksheets

Sometimes students get in the habit of pitching guesses and then working off of that. I prefer to calculate first.

  • Practice 1 - Putting it all together gives the coordinates of the vector.
  • Practice 2 - You can also use this to prove they have a relationship such as parallel or perpendicular.
  • Practice 3 - Find a vector perpendicular to both u = (6, -5, 0) and v = (2, 6, 5).

Math Skill Quizzes

Finding perpendicular vectors seems to baffle a few students. I find that they can't define what "perpendicular" means in most cases.

  • Quiz 1 - Find the angle Θ between the vectors A = (7, 2, 2) and B = (4, -9, 4)?
  • Quiz 2 - See if you can crack what they are looking for here.
  • Quiz 3 - The key to look for here is the angle between them.