Question

The initial and terminal points of a vector are given. Write the vector as a linear combination of the standard unit vectors i and j.

Answer 1

We need to write the given vector as a linear combination of the standard unit vectors i and j.

We know that its initial and terminal points are, respectively:

$(0,-2),(3,2)$

In order to do so, we can subtract its initial point from its terminal point. We obtain:

$\begin{gathered} (3,2)-(0,-2) \\ \\ =\left(3-0,2-\left(-2\right)\right) \\ \\ =\left(3,2+2\right) \\ \\ =\left(3,4\right) \end{gathered}$

Then, since i = (1, 0) and j = (0,1), we have:

$(3,4)=3(1,0)+4(0,1)=3i+4j$

Answer:

$3i+4j$