Search any question & find its solution
Question:
Answered & Verified by Expert
If $p+q+r=0=a+b+c$, then the value of the determinant $\left|\begin{array}{lll}p a & q b & r c \\ q c & r a & p b \\ r b & p c & q a\end{array}\right|$ is
Options:
Solution:
1377 Upvotes
Verified Answer
The correct answer is:
0
We have $\left|\begin{array}{lll}p a & q b & r c \\ q c & r a & p b \\ r b & p c & q a\end{array}\right|$
$\begin{aligned} & \quad=p q r\left(a^3+b^3+c^3\right)-a b c\left(p^3+q^3+r^3\right) \\ & =p q r(3 a b c)-a b c(3 p q r)=0,\end{aligned}$
$\begin{aligned} & \quad=p q r\left(a^3+b^3+c^3\right)-a b c\left(p^3+q^3+r^3\right) \\ & =p q r(3 a b c)-a b c(3 p q r)=0,\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.