Question

I got this question wrong originally and I want to know how to do it right. the correct answer is in the gray box I just don't know how to get that. thank you!

Answer 1

Given that:

$u=-5i+7j,v=9i-j$

Find the sum u+v and subtraction u-v of u and v.

$\begin{gathered} u+v=-5i+7j+(9i-j) \\ =(-5+9)i+(7-1)j \\ =4i+6j \\ u-v=-5i+7j-\mleft(9i-j\mright) \\ =(-5-9)i+(7-(-1))j \\ =-14i+8j \end{gathered}$

For a vector u = a + bi,

$\parallel u\parallel^2=a^2+b^2$

Thus,

$\begin{gathered} \parallel u+v\parallel=4^2+6^2 \\ =52 \\ \parallel u-v\parallel=(-14)^2+8^2 \\ =260 \end{gathered}$

Subtract them to get the desired value.

$\begin{gathered} \parallel u+v\parallel-\parallel u-v\parallel=52-260 \\ =-208 \end{gathered}$