Question

Find the vector and parametric equations for the line through the point P(-4, -2, -5) and the point Q(-5, -5, -1).

Vector Form: r = < , -5 > + t < , 4 >

Answer 1

To find the vector and parametric equations for the line through the points P(-4, -2, -5) and Q(-5, -5, -1), we can use the difference of the position vectors of the two points. The vector equation of the line is r = P + t(Q-P), where P and Q are the position vectors of the points, and t is a scalar parameter.

Step-by-step explanation:

To find the vector and parametric equations for the line through the points P(-4, -2, -5) and Q(-5, -5, -1), we can use the difference of the position vectors of the two points. The vector equation of the line is given by r = P + t(Q-P), where P and Q are the position vectors of the points, and t is a scalar parameter.

In this case, P is the position vector of point P, which is P = -4i - 2j - 5k. Q is the position vector of point Q, which is Q = -5i - 5j - k. By substituting these values, we get the vector equation of the line as:

r = (-4i - 2j - 5k) + t(-1i - 3j + 4k)