Given two points P0(a1, a2, a3) and P1(b1, b2, b3), we have seen in equations (3) and (4...

Given two points P₀(a₁, a₂, a₃) and P₁(b₁, b₂, b₃), we have seen in equations (3) and (4) of §1.2 how to parametrize the line through P₀ and P₁ as r(t) = , where t can be any real number. (Recall that the position vector of an arbitrary point P on the line.)

(a) For what value of t does For what value of t does

(b) Explain how to parametrize the line segment joining P₀ and P₁. (See Figure 1.112.)

(c) Give a set of parametric equations for the line segment joining the points (0, 1, 3) and (2, 5,−7).