Question

I need reminded of this if someone's willing. I know it's so simple, it's driving me crazy that I can't remember.

Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v

Answer 1

\(\bf u = <5, 6>\ v = <-2, -6>
\begin{cases}
-2u\to -2<5,6>\to <-2\cdot 5,-2\cdot 6>\\
\bf 5v\to 5<-2,-6>\to <5\cdot -2,5\cdot -6>
\end{cases}
\\ \quad \\
{\color{brown}{ <a,b>+<c,d>\implies <a+c,b+d>}}\)

meow!

Answer 2

Ah right, thanks dear!

What about this one?

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, 2>, v = <21, 6>

Answer 3

Meow!

Answer 4

Well that would be our friend the dot product :D

\[\large \vec u \cdot \vec v = <u_x,u_y> \cdot <v_x,v_y> = u_xv_x + u_yv_y\] if this comes out to 0, they are orthogonal

Answer 5

And to see if they are parallel we can use that same dot product

\[\large u \cdot v = |u||v|cos\theta\]

if they are parallel, then theta is 0 or 180...so we would just have

\[\large u \cdot v = |u||v|\] or \[\large u \cdot v = -|u||v|\]

Answer 6

Oh okay thanks!

Answer 7

And I feel as though "meow" is a reoccurring theme so "meow" welcome :D