Math  equation of plane and vectors
posted by Shaila .
A plane is defined by the equations x4y+2z=16. Find two vectors parallel to the plane.

You need 3 points.
Probably the easiest ones would be the intercepts
(0,0,8)
(0,4,0) and
(16,0,0)
using the first two, a direction vector would be (0,4,8)
using the last two, a direction vector would be (16,4,0)
we could shorten these to (0,1,2) and (4,1,0)
check:
a normal to our plane is (1,4,2)
taking the dot product of that normal with each of my two vectors yields zero, as expected. 
If i want to find the x, y and z intercepts do i write a new vector equation because we previously found the intercepts but the xintercept =16 yintercept = 4 and the zintercept = 8
i tried writing a vector equation using the one vector as my point and the scalar equation as the direction vector but something seems to be wrong as i do not get the above values!