Determinants Matrices Question 30
Question: For all values of A, B, C and P, Q, R the value of the determinant $ {{(x+a)}^{3}} \begin{vmatrix} \cos (A-P) & \cos (A-Q) & \cos (A-R) \\ \cos (B-P) & \cos (B-Q) & \cos (B-R) \\ \cos (C-P) & \cos (C-Q) & \cos (C-R) \\ \end{vmatrix} $ is
Options:
A) $ 1 $
B) $ 0 $
C) $ 2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have, $ \begin{vmatrix} \cos (A-P) & \cos (A-Q) & \cos (A-R) \\ \cos (B-P) & \cos (B-Q) & \cos (B-R) \\ \cos (C-P) & \cos (C-Q) & \cos (C-R) \\ \end{vmatrix} $
$ \begin{vmatrix} \cos A & \sin A & 0 \\ \cos B & \sin B & 0 \\ \cos C & \sin C & 0 \\ \end{vmatrix}\times \begin{vmatrix} \cos P & \sin P & 0 \\ \cos Q & sinQ & 0 \\ \cos R & \sin R & 0 \\ \end{vmatrix}=0.0=0 $
BETA
