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Exercises Trigonometry

Example 5 from Algebra and Trigonometry, 10.8 Vectors

Adding and Subtracting Vectors

Given $u$ $= 〈 3, - 2 〉$ and $v$ $= 〈 −1, 4 〉,$ find two new vectors u + v, and u − v.

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
To find the sum of two vectors, we add the components. Thus,

$\begin{array}{l} u + v = 〈 3, - 2 〉 + 〈 - 1, 4 〉 \\ = 〈 3 + (- 1), - 2 + 4 〉 \\ = 〈 2, 2 〉 \end{array}$
See Figure 10(a).

To find the difference of two vectors, add the negative components of $v$ to $u .$ Thus,
$\begin{array}{l} u + (- v) = 〈 3, - 2 〉 + 〈 1, - 4 〉 \\ = 〈 3 + 1, - 2 + (- 4) 〉 \\ = 〈 4, - 6 〉 \end{array}$
See Figure 10(b).

Figure 10 (a) Sum of two vectors (b) Difference of two vectors

How did it go?

PreviousShowing That Two Vectors Are Equal Next Performing Scalar Multiplication

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.