Question

Find a vector equation and parametric equations for the line segment that joins p to q. Given p(0, 0, 0) and q(-7, 6, 6), what is the vector equation r(t) and the parametric equations (x(t), y(t), z(t))?

Answer 1

To find the vector equation and parametric equations for the line segment that joins p(0, 0, 0) and q(-7, 6, 6), subtract the coordinates of p from q to find the vector, then write the vector equation using the parameter t, and finally express the parametric equations x, y, and z in terms of t.

Step-by-step explanation:

To find the vector equation and parametric equations for the line segment that joins points p(0, 0, 0) and q(-7, 6, 6), we can use the following approach:

1. Find the vector from p to q by subtracting the coordinates of p from q: v = q - p = (-7, 6, 6) - (0, 0, 0) = (-7, 6, 6).
2. Write the vector equation using the parameter t: r(t) = p + tv = (0, 0, 0) + t(-7, 6, 6) = (-7t, 6t, 6t).
3. Write the parametric equations by expressing x, y, and z in terms of t: x(t) = -7t, y(t) = 6t, z(t) = 6t.