How do you find an equation of a plane in 3-space when you are only given one point and the parametric equation of a line which is contained within the plane? I tried making an augmented matrix but only have 2 equations for 3 unknowns!!!
If you have two vectors that are not parallel, do you know an operation that always produces a third vector that is perpendicular to both of them?I know how it relates to finding the equation. My problem is that I have no clue how to find it:-)
It depends on what information is given. Do you have enough information to determine the two points of intersection between the line and the other two planes?ok. I get that now. What happens if Instead of being given the equation of a line im told that the plane contains a line that intersects two other planes. And then I am given just the equation of the two other planes and a point on the plane that im looking for?
You should be able to find the equation of the line of intersection between the two given planes. Once you have done this, you can solve the rest of the problem exactly as before, as long as the given point doesn't lie on the line.I am not given the equation of a line at all. I am told that two planes (of which the equations are given) intersect at a line. That line passes through another plane. I am given a point in the plane and told to find it's equation> now from what i understand i can't do much with the equations of two planes cause there are three unknown... unl;ess- am i ment to solve in terms of the unkown and use that to choose any two random points and then make vectors to the given point and do what you just told me to do??