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.Initial Point Terminal Point(-7, 1) (9, -3)

Answer 1

$U=16i-4j$

Explanation

any vector in the plane can be writen as a linear combination of the 2 standar unit vectors

$\begin{gathered} i=\langle1,0\rangle\text{ j=}\langle0,1\rangle \\ as\text{ follows} \\ V=\langle a,b\rangle=a\langle1,0\rangle+b\langle0,1\rangle=ai+bj \end{gathered}$

hence

Step 1

component form

$\begin{gathered} U=\text{ terminal point -initial point} \\ U=(9-(-7),(-3-1)=\langle16,-4\rangle \end{gathered}$

now, as a linear combination

$U=16i-4j$

I hope this helps you