P is a point on the line segment joining the points (3,2,-1) and (6,2,-2) . If x coordinate of P is 5, then its y co-ordinate is

Step-by-step solution

Let the points be A(3, 2, -1) and B(6, 2, -2) . The line segment joining A and B can be represented by the parametric equations x = 3 + (6-3)t = 3 + 3t , y = 2 + (2-2)t = 2 , and z = -1 + (-2 - (-1))t = -1 - t , where 0 t 1 . Given that the x -coordinate of point P is 5 , we set 3 + 3t = 5 . Solving for t , we get 3t = 2 , which implies t = 2 3 . Since t = 2 3 lies in the interval [0, 1] , the point P lies on the segment AB . The y -coordinate of any point on this line segment is given by y = 2 + (2-2)t = 2 . There