Question

The orientation of a plane is defined by the direction cosines of

its tangent

its normal

a direction at 45 degree angle to the plane

cannot be defined

​

Answer 1

Answer:

Write the vector, parametric, and symmetric of a line through a given point in a given direction, and a line through two given points.

Find the distance from a point to a given line.

Write the vector and scalar equations of a plane through a given point with a given normal.

Find the distance from a point to a given plane.

Find the angle between two planes.

By now, we are familiar with writing equations that describe a line in two dimensions. To write an equation for a line, we must know two points on the line, or we must know the direction of the line and at least one point through which the line passes. In two dimensions, we use the concept of slope to describe the orientation, or direction, of a line. In three dimensions, we describe the direction of a line using a vector parallel to the line. In this section, we examine how to use equations to describe lines and planes in space.