Question

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

u = <7, 2>, v = <21, 6>

Answer 1

let u and v be two vectors

they are orthogonal if and only if

u dot v = 0

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they are parallel if and only if

v = k*u

where k is some scalar

Answer 2

ok so how do i find u dot v

Answer 3

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

u dot v = a*c + b*d

the * means multiplication between two scalars

u,v are vectors
a,b,c,d are scalars

Answer 4

example

u = <2,3>
v = <7,9>

u dot v = 2*7 + 3*9 = 14 + 27 = 41

Answer 5

"dot" refers to the dot product of two vectors

Answer 6

Ok so for my problem u dot v = 159.

Answer 7

correct

Answer 8

since that result isn't 0, the vectors aren't orthogonal

Answer 9

How would I determine if they are parallel or not?

Answer 10

can you find some scalar k that makes v = k*u true?

Answer 11

does k = 5 make v = k*u true?

ie is v = 5*u true?

Answer 12

Alternate method

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

u and v are parallel if and only if

a/c = b/d

is true

Answer 13

Okay I got 7/ 21 = 2/6 so they are parallel, thanks!

Answer 14

yep they are parallel