What are the normal vectors for these planes? Are they parallel? Are they perpendicular?fazal said:
For two vectors to be parallel, not "the same", one has to be a multiple of the other: <3, 2, 1> and <6, 4, 2> are parallel because <6, 4, 2>= 2<3, 2, 1>.
Why would you need someone else to check for you? Is 5(2)- 3(3)+ 2(-1)= 1?
Is that supposed to be negative? A distance is never negative.
Parallel planes are two planes that never intersect, while coincident planes are two planes that are identical and therefore have an infinite number of points of intersection.
Two planes are parallel if their normal vectors are parallel. This means that the direction of one normal vector is a scalar multiple of the direction of the other normal vector.
Yes, two planes can have different equations but still be coincident if they have the same normal vector and are a distance of 0 units apart.
The distance between two parallel planes can be found by calculating the distance from a point on one plane to the other plane. This can be done by finding the perpendicular distance from the point to the other plane using the formula d = |ax1 + by1 + cz1 + d| / √(a2 + b2 + c2), where the point is (x1, y1, z1) and the plane's equation is ax + by + cz + d = 0.
A point (x0, y0, z0) lies on a plane with equation ax + by + cz + d = 0 if plugging in the values for x0, y0, and z0 into the equation results in a true statement. If the point does not satisfy the equation, then it does not lie on the plane.