Question

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

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

Answer 1

do u knw dot product of two vectors?

Answer 2

noi sorry

Answer 3

no*

Answer 4

@SandeepReddy

Answer 5

you use the dot product

too vectors that are perpendicular

i unit vector (dot) j unit vector

= 0

because A dot B= |A||B|cos X
where x is the angle between the vectors
A dot B = Ax*Bx + Ay*By

thats for two dimension vector

if you have two vectors you can find the coeficients that make them perpendicular by setting the dot product to 0

ai + 3j = A
6i + 1j = B

A dot B = 6 * a + 3 * 1 = 6a + 3

setting it to zero 6a + 3 = 0 implys 6a = -3
a = -1/2


so the vector A is -1/2i + 3j when A is perpendicular to B

The line is parallel hmm have to think

thats the CROSS PRODUCT

WHEN you take the cross product of two vectors that gives

A x B =|A||B|sin X

the function will be zero when the angle X IS 0 OR 180

SINCE THE ANGLE x is the angle between vector A and B

when the cross product is zero the lines are parallel

you can calculate the cross product

| Ax Ay |
| Bx By | = AxBy - AyBx


HOPE THAT HELPS ...

SUMMARIZE

DOT PRODUCT two vectors = 0 when perpendicular

cross product of two vectors is 0 when parallel

Answer 6

thanks so much !

Answer 7

My pleasure!