# Homework Help: Does this line lie in this plane?

1. Sep 20, 2010

### jegues

1. The problem statement, all variables and given/known data
See figure for problem statement. It asks if a given line lies in a given plane.

2. Relevant equations

3. The attempt at a solution

Okay so first I translated the line into its parametric equations and then I subbed those into the equation of the plane respectively.

After simplifying you'll find that,

$$9t-1 = -1$$

Now my solutions manual states the following,

*NOTE* There is no symbol for not-equivalent in tex, so I'm writing NE

$$9t -1 NE -1$$

Why is this so?

Why not let t = 0, and then -1 = -1 and then all will be well in world, no?

What am I missing?

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2. Sep 20, 2010

### gabbagabbahey

\neq works

Each value of $t$ corresponds to a single point on the line. If the entire line were to lie in the plane, the equation would have to be true for all values of $t$ (all points on the line), not just $t=0$