<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Vector Multiplied by a Scalar

Multiplication by a constant which affects magnitude.

Atoms Practice
Estimated7 minsto complete
Practice Vector Multiplied by a Scalar
Estimated7 minsto complete
Practice Now
Transform Vectors

Feel free to modify and personalize this study guide by clicking “Customize.”


Complete the chart.
Word Definition
Vector ____________________________________________________________
____________ the length of a line segment or vector
Scalar ____________________________________________________________
____________ To move a vector on a coordinate system without changing its length or orientation

Multiply by a Scalar

A vector can be multiplied by a real number. This real number is called a _____________.

The product of a vector \begin{align*}\vec{a}\end{align*} and a scalar \begin{align*}k\end{align*} is a vector, written \begin{align*}\vec{ka}\end{align*} . It has the same direction as _____ with a magnitude of ________ if . If \begin{align*}k < 0\end{align*} , the vector has the opposite direction of _____ and a magnitude of ________ .

\begin{align*}\vec{i}\end{align*} is in standard position with terminal point (3, 7) and \begin{align*}\vec{j}\end{align*} is in standard position with terminal point (-2, 4).

  1. Find the coordinates of the terminal point of \begin{align*}5\vec{i} - \vec{j}\end{align*} .
  2. Find the coordinates of the terminal point of \begin{align*}0.2\vec{i} - 0.7\vec{j}\end{align*} .
  3. Find the coordinates of the terminal point of \begin{align*}8\vec{i} + 1.1\vec{j}\end{align*} .


Click here for answers.



Vectors with the same magnitude and direction are ____________. This means that the same ordered pair could represent many different vectors.

Think back: How do you find the slope of a line? _______________________

Are these two vectors equal? 


In each question below, the initial and terminal coordinates for a vector are given. If the vector is translated so that it is in standard position (with the initial point at the origin), what are the new terminal coordinates?

  1. initial (1, 6) and terminal (4, -2)
  2. initial (5, 3) and terminal (1, -6)
  3. initial (8, 4) and terminal (-9, 7)

Find the slope of each vector below with the given terminal coordinates. Assume the vector is in standard position.

  1. terminal (4, 9)
  2. terminal (7, 5)
  3. terminal (-3, 2)


Click here for answers.

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Vector Multiplied by a Scalar.
Please wait...
Please wait...