Josie Jones said:Hi, I am really stuck! I need to find the equation of the plane through the line x=2y=3z perpendicular to the plan 5x+4y-3z=8.
If the book was a textbook on analytic geometry it should have sections on the equations of lines and planes in space, and how to determine the orientation of these objects.Josie Jones said:I don't know how to find a perpendicular line or vector. I think it is a normal vector, but I have not been shown how to do this. I found this question in a book and am unsure how to proceed.
The equation of a plane perpendicular to another plane can be found by taking the cross product of the normal vectors of the two planes. The resulting vector will be the normal vector of the new plane, and the equation can be written in the form ax + by + cz = d, where a, b, and c are the components of the normal vector.
Two planes are perpendicular if their normal vectors are perpendicular, meaning their dot product is equal to 0. This can also be checked by finding the angle between the normal vectors, which should be 90 degrees.
No, two planes cannot have the same equation and be perpendicular. This is because the normal vectors of the planes would be parallel, meaning their dot product would not be equal to 0.
Yes, it is possible for a line to be perpendicular to a plane. This occurs when the line is parallel to the normal vector of the plane, meaning their dot product is equal to 0.
There are infinitely many planes that can be perpendicular to a given plane. This is because the normal vector of the given plane can be multiplied by any scalar value to create a new normal vector, and therefore a new plane.