Question

Find a vector equation for the line through the point P = (1, -5, -5) and parallel to the vector v = (-1, 2, 1).

Assume r(0)=1i-5j-5k and that v is the velocity vector of the line.

Answer 1

The vector equation for the line through point P(1, -5, -5) and parallel to vector v(-1, 2, 1) is r = (1, -5, -5) + t(-1, 2, 1).

Step-by-step explanation:

To find a vector equation for the line through point P(1, -5, -5) and parallel to vector v(-1, 2, 1), we can use the point-slope form of a line equation. The equation is given by r = r0 + tv, where r is the position vector, r0 is the given point, t is a scalar, and v is the direction vector.

Substituting the given values, the vector equation becomes:

r = (1, -5, -5) + t(-1, 2, 1)

This is the vector equation for the line through point P and parallel to vector v.