If α neq a, β neq b, γ neq c and begin matrix α & b & c \a & β & c \a & b & γ \\end matrix =0 , then frac a α- a +frac b β- b +frac γ γ- c is equal to :

Mathematics · Determinants

JEE Main 2024 — 8 April, Shift 2 — Question 3

If $\alpha \neq a, \beta \neq b, \gamma \neq c$ and $\left| \begin{matrix}\alpha & b & c \\a & \beta & c \\a & b & \gamma \\\end{matrix} \right|=0$ , then $\frac{\mathrm{a}}{\alpha-\mathrm{a}}+\frac{\mathrm{b}}{\beta-\mathrm{b}}+\frac{\gamma}{\gamma-\mathrm{c}}$ is equal to :

Option A:
2
Option B:
3
Option C:
0
Correct
Option D:
1

Answer: C

Step-by-step solution

$\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-\mathrm{R}_{2}, \mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{3}$

$\left| \begin{matrix}\alpha -\text{a} & \text{b}-\beta & 0 \\0 & \beta -\text{b} & \text{c}-\gamma \\\text{a} & \text{b} & \gamma \\\end{matrix} \right|=0$

$(\alpha-a)(\gamma(\beta-b)-b(c-\gamma))-(b-\beta)(-a(c-\gamma))=0$

$\gamma(\alpha-a)(\beta-b)-b(\alpha-a)(c-\gamma)+a(b-\beta)(c-\gamma)$

$\frac{\gamma}{\gamma-c}+\frac{b}{\beta-b}+\frac{a}{\alpha-a}=0$

Answer key and solution verified before publishing.

Practise Determinants

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 8 April, Shift 2
Subject: Mathematics
Chapter: Determinants
Topic: Determinants

If the system of equations x+4 y-z=lambda , 7 x+9 y+mu z=-3,5 x+y+2 z=-1 has infinitely many solutions, then (2 mu .+3 lambda) is equal to :

Answer: C

Step-by-step solution

Practise Determinants

More Determinants questions from this paper