Question

Given the vectors u =-7j and w=-9i+4j, find 8u and u+w.Write your answers in the form ai+bj.

Answer 1

Recall that:

$\begin{gathered} \text{For all a, b, c, d, e real numbers:} \\ (ai+bj)+(ci+dj)=(a+c)i+(b+d)j, \\ e(ai+bj)=(ea)i+(eb)j\text{.} \end{gathered}$

Therefore:

$\begin{gathered} 8u=8(-7j)=8(0i-7j)=(8\cdot0)i+(8\cdot(-7))j=0i-56j=-56j\text{.} \\ u+w=(-7j)+(-9i+4j)=(0i-7j)+(-9i+4j)=(0-9)i+(-7+4)j \\ =-9i-3j\text{.} \end{gathered}$

Answer:

$\begin{gathered} 8u=-56j\text{.} \\ u+w=-9i-3j\text{.} \end{gathered}$