Question

If a, b, c are non-zero real numbers, then $\left| \begin{matrix} bc & ca & ab \\ ca & ab & bc \\ ab & bc & ca \end{matrix} \right|$vanishes when,

• A. $\frac{1}{a}$– $\frac{1}{b}$ – $\frac{1}{c}$ = 0
• B. $\frac{1}{a}$+ $\frac{1}{b}$ + $\frac{1}{c}$= 0
• C. $\frac{1}{b}$ – $\frac{1}{c}$ – $\frac{1}{a}$ = 0
• D. $\frac{1}{b}$ – $\frac{1}{c}$ – $\frac{1}{a}$ = 0

Answer 1

Answer: (B)

$\frac{1}{a}$+ $\frac{1}{b}$ + $\frac{1}{c}$= 0

Answer 2

$\left| \begin{matrix} bc & ca & ab \\ ca & ab & bc \\ ab & bc & ca \end{matrix} \right|$ = 0

3a²b²c² – [(ab)³ + (bc)³ + (ca)³] = 0

Ž (ab + bc + ca) (a²b² + b²c² + c²a² – ab²c – bc²a – ca²b) = 0 Ž ab + bc + ca = 0 Ž $\frac{1}{a}$+ $\frac{1}{b}$ + $\frac{1}{c}$ = 0