what is the equation of a plane containing a given line and parallel to the x-axis??

Question

well this is a question i was unable to do.. we have to find the equation of a plane.. which is parallel to x-axis and we have the vector equation of the line.. so we need to cross product the direction vector of line and the other parallel vector to find the normal vector.. and then find the plane eq with the given pt on the line.. but the problem is what is the equation of the part.. PLANE PARALLEL TO X-AXIS? what will we denote it as and why???? help me ppllll

Answer 1

Your question: PLANE PARALLEL TO X-AXIS? what will we denote it as and why????
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The general equation of a plane is
ax + b y + cz + d = 0
where a, b, c and d are constants.

Now consider specific cases, when one, two or even three of the constants =0.

For example which plane has equation x=0 ? (In 3-dimensional space of course.)

Imagine it! It is a plane defined by axes y and z! (Because for all points of that plane x=0.)

Now consider the plane with constant a=0.

The equation of that plane is

by + cz + d = 0.

Imagine that plane. Remember we are in 3-dimensional space. Think it over. Now we are very close to answer your question ...

Answer 2

Once you find the normal vector, it should look like or some other similar notation.

Then the plane's equation is ax + by + cz + d = 0, where the a,b, and c are just the components of the normal vector.
Then plug the known point into x,y, and z in the equation to determine the value of d.

If you want, you can solve it for z, but usually the equation of planes are left in the above format so one could easily derive the normal vector the other way just by looking at it.

Answer 3

y= something
like y= 3

Answer 4

what