Question

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

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

Answer 1

Let

u = <a,b>
v = <c,d>

the dot product of u and v is

u dot v = a*c + b*d

if the dot product of u and v is 0, then u is orthogonal (ie perpendicular) to v.

Answer 2

it is orthogonal, correct?

Answer 3

u is parallel to v if and only if u = k*v for some scalar k

u = k*v
<a,b> = k*<c,d>
<a,b> = <k*c,k*d>
a = k*c and b = k*d
k = a/c and k = b/d
a/c = b/d

All that work above shows that IF a/c = b/d, then u and v are parallel. They either point in the same direction, or they point in complete opposite directions.

Answer 4

`it is orthogonal, correct?`
yes that is correct

u dot v = a*c + b*d
u dot v = 6*8 + (-2)*24
u dot v = 48 + (-48)
u dot v = 0

so they are indeed orthogonal

Answer 5

thank you!!!

Answer 6

sure thing