Find both the vector equation and the parametric equations of the line through (4,5,5) that is perpendicular to the lines x = 3 - 2t, y = 4 + 4t, z=3 - 6t and x= - 2t, y = 4+ t, z=3-t, where t=0 corresponds to the given point. The vector equation is (x,y,z) = ( 4 , 5, 5) + t(2, 10,6). Find the parametric equations of the line through (4,5,5) in the direction of the vector v = u xw. The parametric equations are x = |, y = ]. z = . (Use the answer from the previous step to find this answer.) Determine whether the following pair of lines is parallel, intersects at a single point, or is skew. If the lines are parallel, determine whether they are the same line (and thus intersect at all points). If the lines intersect at a single point, determine the point of intersection. r= (4,1,2) + 1(7, -9,3) R= (10,7,20) + s (2,2,6) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The lines intersect at the single point ( ) (Simplify your answers.) O B. The lines are skew. O C. The lines intersect at all points on the line r(t). O D. The lines are parallel. Determine whether the following pair of lines is parallel, intersects at a single point, or is skew. If the lines are parallel, determine whether they are the same line (and thus intersect at all points). If the lines intersect at a single point, determine the point of intersection. x = 3, y=7 -t, z= 1 +t and x= -5 - 8s, y=1 + 6s, z=5 -s Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The lines intersect at the single point ( ) (Simplify your answers.) O B. The lines are parallel. O C. The lines are skew. O D. The lines intersect at all points on the line r(t). Find the equation for the plane through Po( - 9,5, - 5) perpendicular to the following line. x = - 9 +t, y= 5 + 2t, z= 4t, - co