nameVoid said:
If the point <x, y, z> lies in the plane, what do you have to subtract to get a vector parallel to the plane?nameVoid said:
nameVoid said:
A line is a one-dimensional geometric figure that extends infinitely in both directions. It has no width or depth. A plane, on the other hand, is a two-dimensional surface that extends infinitely in all directions. It has length and width, but no depth.
For a line, an equation in the form y = mx + b can be used, where m is the slope of the line and b is the y-intercept. For a plane, an equation in the form ax + by + cz = d can be used, where a, b, and c are the coefficients of x, y, and z, respectively, and d is a constant.
To find the equation of a line perpendicular to another line, you can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. So, if the slope of the original line is m, the slope of the perpendicular line would be -1/m. You can then use this slope and a point on the line to write the new equation.
If two planes are parallel, they will have the same normal vector. To find the normal vector of a plane, you can use the coefficients of the x, y, and z terms in the plane's equation. If the normal vectors of two planes are equal, then the planes are parallel.
In 3-dimensional space, a line can be uniquely determined by two points, and a plane can be uniquely determined by three points that are not collinear. This means that they cannot all lie on the same line.