Question

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

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

Answer 1

get their dot product
if their dot product is 0, they're orthogonal

if one vector is just a multiple of the other... then they're parallel

Answer 2

To get their dot product, do you multiply or add them together?

Answer 3

actually... both you multiply them, and then you add them =)

\(\bf <a,b>\cdot <c,d>\implies a\cdot c+b\cdot d\)

Answer 4

so its <6,-2> x <8,24>
(6 x 8) + (-2 x 24)
<42,-48>

Answer 5

well.... is supposed to give you a constant... no a vector \(\large \bf \bf <a,b>\cdot <c,d>\implies a\cdot c+b\cdot d\)

Answer 6

so its just (6 x 8) + (-2 x 24) ?
how does that work?

Answer 7

yeap

Answer 8

So how do I know if thay are parallel orthogonal or neither>

Answer 9

get their dot product
if their dot product is 0, they're orthogonal

if one vector is just a multiple of the other... then they're parallel

Answer 10

<42,-48>
Is that the dot product?

Answer 11

well.... is supposed to give you a constant... no a vector though \(\large \bf \bf <a,b>\cdot <c,d>\implies a\cdot c+b\cdot d\)

Answer 12

So the vector is <42,-48>?
or is it -6? which isnt zero or a multiple... So neither?

Answer 13

hmmm recheck your dot product

Answer 14

but the dot product gives a constant.. not a vector though

Answer 15

<48, -48> equals zero
orthogonal!

Answer 16

yea 48 - 48 yes... is the dot product.. and that's 0, thus they're orthogonal, "perpendicular", then

Answer 17

AH! Thank you! Quick question- when doing dot products with three numbers each, is it the same thing?

Answer 18

yes

Answer 19

http://www.learningaboutelectronics.com/images/Dot-product-of-vectors.png

Answer 20

Thank you!

Answer 21

yw