Question

Find the component form of the indicated vector

Answer 1

(d) (12, -34)

Explanation:

You want the component form of the vector sum -3u +5v where u=(1,3) and v=(3,-5).

Vector sum

Add the corresponding parts of the scaled vectors. The scale factor applies to both vector components. (It works the same way as "dilation".)

-3u +5v = -3(1, 3) +5(3, -5)

= (-3, -9) +(15, -25) = (-3 +15, -9 -25)

= (12, -34)