Posted by **Shaila** on Sunday, September 5, 2010 at 11:27pm.

A plane is defined by the equations x-4y+2z=16. Find two vectors parallel to the plane.

- Math - equation of plane and vectors -
**Reiny**, Sunday, September 5, 2010 at 11:42pm
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.

- Math - equation of plane and vectors -
**Shaila**, Tuesday, September 7, 2010 at 12:41pm
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 x-intercept =16 y-intercept = -4 and the z-intercept = 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!

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