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Mathematics Question on Applications of Determinants and Matrices

If △=∣345x 456y 567z xyz0∣=0\text{If}\ \triangle = \begin{vmatrix} 3 & 4 & 5 & x \\\ 4 & 5 & 6 & y \\\ 5 & 6 & 7 & z \\\ x & y & z & 0 \end{vmatrix} = 0

A

x,y,z are in A.P

B

x,y,z are in G.P

C

x,y,z are in H.P

D

none of these

Answer

x,y,z are in A.P

Explanation

Solution

The correct option is (A): x,y,z are in A.P