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Exercises Trigonometry

Example 7 from Algebra and Trigonometry, 10.8 Vectors

Using Vector Addition and Scalar Multiplication to Find a New Vector

Given $u$ $= 〈 3, - 2 〉$ and $v$ $= 〈 - 1, 4 〉,$ find a new vector w = 3u + 2v.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, we must multiply each vector by the scalar.
$\begin{array}{l} 3 u = 3 〈 3, - 2 〉 \\ = 〈 9, - 6 〉 \\ 2 v = 2 〈 - 1, 4 〉 \\ = 〈 - 2, 8 〉 \end{array}$
Then, add the two together.
$\begin{array}{l} w = 3 u + 2 v \\ = 〈 9, - 6 〉 + 〈 - 2, 8 〉 \\ = 〈 9 - 2, - 6 + 8 〉 \\ = 〈 7, 2 〉 \end{array}$
So, $w$ $= 〈 7, 2 〉 .$

How did it go?

PreviousPerforming Scalar Multiplication Next Finding the Components of the Vector

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.8, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.