Question

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

u = <3, 0>, v = <0, -6>

Answer 1

if u & v are paralell then 1 vector must be the scalar multiple of the other vector.
if u & v are orthogonal then their dot product must be equals to zero.

Answer 2

make sense?

Answer 3

Um no, I'm confused. I didn't learn any of this.

Answer 4

scalar multiple means that one vector is the multiple of the other:
for example:
\[<2,4>\]
is the vector & its scalar multiple is :
\[<1,2>\]
i.e,\[<2,4>=2<1,2>\]

Answer 5

get it?

Answer 6

you can see that :
\[<3,0>\neq <0,-6>\]
so they are not the scalar multiples of each other
i.e, they are not paralell.

Answer 7

dot product is the property of vectors which says that product of two vectors gives a scalar quantity.
i.e. \[i.i=1\]
\[j.j=1\]
\[k.k=1\]
where i,j,k are the unit vectors along x,y,z directions.

Answer 8

make sense?

Answer 9

So wait, they're orthogonal, then?

Answer 10

orthogonal have a condition that :
if two vectors are orthogonal then their dot product must be zero
i.e,
\[<3,0>.<0,-6>=0\]

Answer 11

& most important is
\[i.j=j.k=k.i=o\]

Answer 12

yes they are orthogonal.
because the given two vectors have dot product equals zero

Answer 13

Thanks!

Answer 14

pleasure!