Vector Equations in SpaceAccelerated Math 3

Vector r is the position vector to a variable point P(x,y,z) on the line. Point Po=(5,11,13) is a fixed point on the line. Unit vector u points along the line. Let d be the directed distance from Po to P. Thus , the displacement vector from Po to P is oP P du

Note that the position vector r to the variable point is the sum of and the position vector to the fixed point.

du

oP

or P du

Ex. 1 Find the particular equation of the line that contains the fixed point Po=(5,11,13) and is parallel to the unit vector 3 6 2

7 7 7u i j k

Ex. 2 Find the point on the line in ex. 1 that is at a directed distance of -21 from Po.

Ex. 3 Find the point where the line in ex.1 intersects the xy-plane.