Question

Find the ratio in which the points join A(2, 1, 5) and B(3, 4, 3) is divided by the plane 2x + 2y – 2z = 1. Also, find the coordinates of the point of division.​

Answer 1

Let point C is on the line joining A(2, 1, 5) and B(3, 4, 3) which is divided by the plane 2x + 2y – 2z = 1.

• Let k:1 in which line is divided. Therefore the point is

       C ${(\frac{3k+2}{k+`1} ),(\frac{4k+1}{k+1}) ,(\frac{3k+5}{k+1})}$

• C lies on the plane 2x+2y-2z=1, therefore gonna satisfy the question.

        -> 2x+2y-2z =1

            2 (x+y-z) = 1

            2  $(\frac{3k+2}{k+1} + \frac{4k+1}{k+1} + \frac{3k+5}{k+1})$  = 1

            2  ( 3k+2 + 4k+1 - 3k-5 ) = k+1

            6k + 4 + 8k + 2 - 6k+ 10 = k+1

            8k - 4 = k+1

            7k = 5

            k = $\frac{5}{7}$

         Therefore the ratio is 5/7

• Put values of k in C(q,w,e) will give co-ordinates of the point.  

       C $(\frac{3k+2}{k+1} + \frac{4k+1}{k+1} + \frac{3k+5}{k+1})$ ( k = 5/7 )

      = C $(\frac{27}{12} + \frac{27}{12} + \frac{50}{12})$