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

Step-by-step solution

Let the points be A(3, 5, -1) and B(6, 3, -2) . The line passing through A and B can be represented in parametric form. Let P divide the segment AB in the ratio k:1 . The coordinates of P are given by the section formula: P = ( 6k + 3 k + 1 , 3k + 5 k + 1 , -2k - 1 k + 1 ) Given that the y -coordinate of P is 2 , we set the y -component equal to 2 : 3k + 5 k + 1 = 2 3k + 5 = 2(k + 1) 3k + 5 = 2k + 2 k = -3 Now, substitute k = -3 into the expression for the x -coordinate of P : x = 6(-3) + 3 -3 + 1 x = -18 + 3 -2 x