Vectors

[cunning falcon]

what is the normal vector of the plane x - 2y = 0?

bc if u work that out, yk that v will be perpendicular to that normal vector, and u can use the definition of the dot product to find information about a, b and c

[ripe sierra]

isnt it just (1,-2,0)

[ripe sierra]

so i know that the +ve z axis is (0,0,1) and cos60=1/2 and also dot producting abc with (1,-2,0) =0. But i got a pile of info that idk how to link.

[cunning falcon]

yeah

[ripe sierra]

im not sure what to dot product tho

[cunning falcon]

use the fact that a . b = |a||b|cosθ

[ripe sierra]

are we leaving v as (a,b,c)?

[cunning falcon]

yeah

so v . (unit vector in z direction) = cos(60)

from there u should be able to solve for a, b and c hopefully

may have to use the fact that the magnitude is 1

[ripe sierra]

i got 3c^2=a^2+b^2

what does size 1 even mean in this context

[cunning falcon]

it means a^2 + b^2 + c^2 = 1

[ripe sierra]

oh yh i tried that

but how do i solve 3 unkowns