Question

P, Q, R, S are four coplanar points on the sides AB, BC, CD, DA of a skew quadrilateral. The product $\frac{AP}{PB}$.$\frac{BQ}{QC}$.$\frac{CR}{RD}$.$\frac{DS}{SA}$ equals –

• A. –2
• B. –1
• C. 2
• D. 1

Answer 1

Answer: (C)

2

Answer 2

Let the vertices A, B, C, D quadrilateral be

(x₁, y₁, z₁), (x₂, y₂, z₂), (x₃, y₃, z₃) & (x₄, y₄, z₄) and the equation of plane PQRS be

u ŗ ax + by + cz + d = 0

let u_r = a_r x + b_r y + c_r z + d where r = 1, 2, 3, 4

Then $\frac{AP}{PB}.\frac{BQ}{QC}.\frac{CR}{RD}.\frac{DS}{SA}$

= $\left( - \frac { u _ { 3 } } { u _ { 4 } } \right)$ $\left( - \frac{u_{4}}{u_{1}} \right)$ = 1.