Parallel ski tracks on a slope
Floors in a multi-story building
Train tracks converging at a point
Intersections of streets in a city grid
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Show they intersect at a right angle
Demonstrate they are coplanar but intersect
Show they have the same direction vector or that the angles between them and a transversal line are equal
Prove they are concentric circles
Yes, if they are equidistant from each other
No, skew lines do not lie in the same plane
Yes, if they are equidistant from the plane at some point
It depends on the angle of skew
Vectors are used to measure angles directly between lines
Vectors help describe the direction of lines or planes; if direction vectors are scalar multiples, they indicate parallelism
Vectors can show where lines intersect with no need for equations
Vectors directly determine the slope of a plane
They converge at a distant point
They are perpendicular to each other
Two lines are parallel if they lie in the same plane and do not intersect, or if they are coplanar and equidistant from each other
They are curving away from each other
Two planes are perpendicular if the angle between them is 90 degrees, or if a normal vector to one plane is parallel to the other plane
They are perpendicular if they are equidistant at all points
They intersect at any angle other than 90 degrees
They do not intersect at all
The planes form a circle of intersection
The planes merge into a single vertical line
The lines of intersection will be parallel to each other
They create an infinite number of intersection lines
Parallel planes have equations of the form ax + by + cz = d1 and ax + by + cz = d2, where the coefficients of x, y, and z are the same
Planes are parallel if their equations are opposites
Their slope equations must be equal
Each of their normal vectors must be perpendicular to each other
A line is parallel to a plane if they do not intersect or if the line is contained in a plane parallel to the given plane
If they share a common point but diverge elsewhere
By ensuring the line's equation is a multiple of the plane's equation
If the line's gradient is exactly opposite the plane's angle