Question

1. Consider three position vectors (tails are the origin):
→− u =⟨1,0,0⟩
→− v =⟨4,0,2⟩
→− w = ⟨0, 1, 1⟩
(a) Find an equation of the plane passing through the tips of u , v , and w .
(b) Find an equation of the line perpendicular to the plane from part (a) and passing
through the origin.

Part (a) normal vector is <-2,-5,3>
Not understanding how to use (0,0,0) to find line equation for part b
Also equation of plane is -2(x-1)-5(y-0)+3(z-0)=0

Answer 1

??? was having login in issues...

Answer 2

ok, show me your work in part a)

Answer 3

take The cross product of uv X uw to find the normal vector V
so cross product is

Answer 4

so equation is -2(x-1)-5(y-0)+3(z-0)=0 by the formula

Answer 5

i do the cross product in detail but too long to write

Answer 6

so, for part a, your equation should be 2x +5y -3z =2, right?