Question

Determine whether u and v are orthogonal, parallel, or neither.
u=<1,2,-3>
v=<(-4/3), (-8/3), 4>
I dont understand how to do this. Can someone please help?

Answer 1

hint : two vectors are parallel if the components form same ratio

Answer 2

What does that mean? I am sorry, I am not that great when it comes to vectors.

Answer 3

take the ratio of each component

Answer 4

ratio of x components : 1/(-4/3) = ?
ratio of y components : 2/(-8/3) = ?
ratio of z components : -3/4 = ?

Answer 5

if u get same number for all of them, then the vectors are parallel

Answer 6

do you know how to take the dot product?

Answer 7

The vectors are parallel. They all equaled the same number. Can you explain to me why they are parallel? Thanks

Answer 8

if the vectors are parallel, then we can write
\(\large \vec{v} = t \vec{u}\)

t is a scalar

Answer 9

right ?

Answer 10

say \(\large \vec{v} = <a_1, a_2, a_3>\),
\(\large \vec{u} = <b_1, b_2, b_3>\)

for them to be parallel :
\(\large \vec{v} = t \vec{u} \)

=>

\(\large <a_1, a_2, a_3> = t<b_1, b_2, b_3>\)
\(\large <a_1, a_2, a_3> = <tb_1, tb_2, tb_3>\)

compare the components both sides
\(\large a_1 = tb_1\)
\(\large a_2 = tb_2\)
\(\large a_3 = tb_3\)

Answer 11

^^if u take the ratio of components u wud get the same number \(t\)

Answer 12

So they are parallel then? Thats what I have been getting.

Answer 13

yup!

Answer 14

Alright thanks! I really appreciate your help!

Answer 15

np :)
see if u can reply to turingtest's question above... on dot product..