Question

If R is (-4, 7) and S is (-2, 12), what is the component form of the vector R.S?

(8,84)
(2,5)
(-6, 19)
(-3,9.5)

Answer 1

(2, 5)

Explanation:

Given:

• R = (-4, 7)
• S = (-2, 12)

To find the components of
`\overrightarrow{RS}` we need to go from R to O and then O to S. Remember that
`\overrightarrow{RO}` is the negative of
`\overrightarrow{OR}`. Therefore:

`\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}`

Therefore, the component form (x, y) of the vector
`\overrightarrow{RS}` is (2, 5)