Question

If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is

• A. 0
• B. 1
• C. 2
• D. 4pqr

Hint:

Zero determinant often indicates linear dependence or proportional rows.

Answer 1

The Correct Option is B

The determinant being zero implies proportionality of rows, giving: (p)/(x)=(q)/(y)=(r)/(z) Let each ratio be k. Then: (p)/(x)+(q)/(y)+(r)/(z)=3k From proportionality conditions, k=\tfrac13. Hence sum =1.