Question

Find a vector equation and parametric equations for the line segment that joins P to Q.

P(3.5, −2.2, 3.1), Q(1.8, 0.3, 3.1)

Answer 1

The vector equation is r = P + tD, where P is the position vector of point P, r is the position vector of any point on the line, and t is a scalar parameter. The parametric equations can be obtained by writing the x, y, and z coordinates of the position vector r in terms of t.

Step-by-step explanation:

To find a vector equation for the line segment that joins points P and Q, we can subtract the coordinates of Q from those of P to get the direction vector. Let's call this vector D. The vector equation is given by:

r = P + tD

Where P is the position vector of point P, r is the position vector of any point on the line, and t is a scalar parameter that varies from 0 to 1. The parametric equations can be obtained by writing the x, y, and z coordinates of the position vector r in terms of t.

x = 3.5 + (1.8 - 3.5)t

y = -2.2 + (0.3 + 2.2)t

z = 3.1 + (3.1 - 3.1)t