Question

If \[ \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0, \] then the value of \(\dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z}\) is

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(4pqr\)

Hint:

Use row/column operations to simplify determinants quickly.

Answer 1

The Correct Option is B

Step 1: Apply column operations to simplify determinant.
Step 2: Determinant zero implies linear dependence.
Step 3: Result gives: \[ \frac{p}{x}+\frac{q}{y}+\frac{r}{z}=1 \]