What is the equation of the surface obtained by revolving the line $\frac{x}{1}=\frac{y}{1}=\frac{z}{0}$ about $x$ axis?
So I have a plane passing through the points $(0,0,0)$ and whose normal has direction ratios $1,1,0$
Now I am having trouble understanding how to rotate it about $x$ axis? How to rotate a plane about the $x$ axis.
Can someone please help me solve it. Any hints will be sufficient
This line locates on x-y plane (because the gradient of z is $0$) and it's equation is $y=x$. It passes the origin and its rotation around x axis produces a conic surface with its vertex at the origin. It's called a right circular cone with axis along the x-axis and its equation is $x^2=y^2+z^2$. Its cross section with x-z plane is a line with equation $z=x$. The line $y=x$ is called the generator and it makes an angle of $45^o$ with the axis of the cone.
Note: If you wand to find how this equation if found you can go to page 632, Quadratic surfaces, Calculus, Robert A, Adams.