Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = < 1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =

Answers: 

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t> 
- parametric equations:   
      x = 1 + 6t
      y = -1 + 7t
      z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
   = (7,6,1) - (1,-1,7)
v  = (6, 7, -6)

The vector equation of the line is given by



Where

= a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by



In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by 



The parametric equations of the line are given by: