Question

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

u = <6, -2>, v = <8, 24>

Answer 1

the vectors are orthogonal if the result is 0 after using the dot product.
\[u \cdot v =<u_1v_1,u_2v_2,...u_nv_n> \]

Answer 2

If vectors are parallel, then there exists a scalar \(c\) such that\[
\mathbf u = c \mathbf v
\]

Answer 3

\[u \cdot v = <u_1v_1+u_2v_2+...u_nv_n>\]

for dot product

but if it's neither than the dot product can't be 0 and a scalar c doesn't exist.

Answer 4

do i just plug in the numbers to solve?

Answer 5

you could.. since we have
\[u=<u_1,u_2>, v=<v_1,v_2>\]
and we can use dot product
\[u \cdot v = <u_1v_1+u_2v_2+...u_nv_n> \]

Answer 6

u= <6,-2> and v = <8,24>
\[u_1=6,u_2=-2,v_1=8,v_2=24 \]
now we plug those values into the dot product formula
\[u \cdot v = u_1v_1+u_2v_2\]

Answer 7

\[u \cdot v = (6)(8)+(-2)(24) \]

Answer 8

so what is 6 x 8
and
what is -2 x 24 ?

Answer 9

6x8=48
-2x24= -48

Answer 10

mhm
\[u \cdot v = 48-48 \]
so now what's 48-48?

Answer 11

0. so is it neither?

Answer 12

no.. since our dot product is 0, our vectors are _______________

Answer 13

orthogonal since it equal 0

Answer 14

yes :)