mmm seems easy when u use this p=b=c=0
If \begin{vmatrix} p & b & c\\ a & q & c\\ a& b & r \end{vmatrix}=0
find the value of pp-a + qq-b + rr-c
where a≠p. b≠q , and c≠r
ans---- 2
-
UP 0 DOWN 0 0 4
4 Answers
\begin{vmatrix} p &b &c\\ a &q &c \\ a &b &r \end{vmatrix}
R2-------------->R2 - R3
\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a &b &r \end{vmatrix}
R3-------------->R3 - R1
\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a-p &0 &r-c \end{vmatrix}
Taking (p-a)(q-b)(r-c)common from C1, C2, C3 respectively we get....
(p-a)(q-b)(r-c)\begin{vmatrix} \frac{p}{p-a} &\frac{b}{q-b} &\frac{c}{r-c}\\ 0 &1 &-1 \\ -1 &0 &1 \end{vmatrix}
expanding along R1
pp - a + bq - b + cr - c = 0
or
pp - a + b + q - qq - b + c + r - rr - c = 0
or
pp - a + qq - b - 1 + rr - c - 1 = 0
or..
pp - a + qq - b + rr - c = 2
answer....