Question

The ratio in which the join of A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z-1=0 is .

• A. 5:7
• B. 7:5
• C. 3:5
• D. 5:3

Answer 1

The correct option is A 5:7

Let the given plane divides the join of AB in k:1 at point C.
Hence, the coordinates C using Section Formula will be:
$(\frac{3k+2}{k+1},\frac{4k+1}{k+1},\frac{3k+5}{k+1})\mathrm{Since},\mathrm{point}C\mathrm{lies}\mathrm{on}\mathrm{given}\mathrm{plane}\Rightarrow 2\left(\frac{3k+2}{k+1}\right)+2\left(\frac{4k+1}{k+1}\right)-2\left(\frac{3k+5}{k+1}\right)=1\mathrm{On}\mathrm{solving},\mathrm{we}\mathrm{get}-8k-4=k+1\Rightarrow k=\frac{5}{7}\mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{ratio}\mathrm{is}5:7.$