Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point Q(-3, 0, -7). Vector Form: r = , -5 ) + t( ,-2) Parametric form (parameter t, and passing through P when t = 0): a = x(t) = y = y(t) = z = z(t) =

Please give as much as detail as possible. Find the parametric equations of the line which passes through the point (2,0,-3) in the direction of the vector v = <0,-1,5> and find the distance between the point (-3,1,-5) and this line.

3 4 33. Determine the vector equation, parametric equations, and, if possible, symmetric equation of the line that passes through the point P(1, 3, 5) and a. has direction vector (-2, -4, -10) b. also passes through the point Q(-7, 9, 3) c. is parallel to the line that passes through R(4, 8, -5) and S(-2, -5,9) d. is parallel to the .x-axis e. is perpendicular to the line (x, y, z) = (1, 0, 5) + (-3, 4, -6) f. is perpendicular to the plane determined by the points A(4, 2, 1), 4 2), and C(-3, 2, 1) nd 59 nsv of -3 of the plane that