question_answer

If \[p+q+r=0=a+b+c\], then the value of the determinant is

A) 0        

B) \[pa+qb+rc\]

C) 1                   

D) none of these

Correct Answer: A

Solution :

[a] \[=pqr({{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc)-\] \[abc({{p}^{3}}+{{q}^{3}}+{{r}^{3}}-3pqr)\] \[=pqr(a+b+c)({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca)\] \[-abc (p+q+r)({{p}^{2}}+{{q}^{2}}+{{r}^{2}}-pq-qr-pr)\] = 0