Vectors help needed Please help

Question

waheguru · Answer

How do I approach this problem?

amistre64 · Answer

define colinear ...

waheguru · Answer

Ill draw it|dw:1430855492081:dw|

waheguru · Answer

its when they are on the same line, but it doesnt matter what directon they face

amistre64 · Answer

so, let x = ky  for some scalar k

amistre64 · Answer

in fact, x = 3ky

waheguru · Answer

collinear, vectors that are parallel and that lie on the same straight line

waheguru · Answer

ok

amistre64 · Answer

x = 3k y  is colinear

mx + ny = 0,  solve

waheguru · Answer

how?

waheguru · Answer

there are so many variables

amistre64 · Answer

substitution of course ...

amistre64 · Answer

x and y arent variables, they are vectors

waheguru · Answer

Why is there "k"

amistre64 · Answer

how else are you going to scale a vector?  its just whats in my head.  it may be unnecessary but unless otherwise contrived, lets stick with it :)  its a work in progress

mx + ny = 0

m (3k y) + ny = 0

(3km + n) y = 0

amistre64 · Answer

k is either 1 or -1

amistre64 · Answer

if y = (1,0),  x= (-3,0) or (3,0) in order to be colinear right?

amistre64 · Answer

if x is not a scalar multiple of y, then x and y are independant

the only solution to a linear combination of independant vectors such that:

$$a_1\vec{x_1}+a_2\vec{x_2}+...+a_n\vec{x_n}=0$$
is if all the values of a1 thru an = 0

amistre64 · Answer

split it into cases if the k bothers you

case 1:  x = 3y
case 2:  x = -3y