- #1

kent davidge

- 933

- 56

## Homework Statement

What's the vector equation for a plane which contains the point ##(-2,2,1)## and whose vectors ##(1,1,2)## and ##(2,1,-1)## are parallel to it?

## Homework Equations

I think the relevant here is

- The plane equation.

## The Attempt at a Solution

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We can go through demanding that a vector on it can always be expressed as ##(-2,2,1) + a(1,1,2) + b(2,1,-1)## but I did in a different manner.

I first took the vector product of the two given vectors, which is ##(-3,5,-1)## and then constructed the equation of the plane, passing on the given initial point ##(-2,2,1)##. It is ##-3(x+2)+5(y-2)-(z-1) = 0##. Then I considered an arbitrary point in the plane having "coordinates" ##(a,b,c)## and I substituted these components into the equation above. Calling the "point" (vector) ##P## I ended up with ##P(t,u) = (t,u,-3t+5u-15)## with ##\{t,u \} \in \mathbb{R}##.

It seems to satisfy the plane equation as it's constructed to satisfy it. Never the less, I would like to know whether this is a valid answer or not.