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In a triangle ABC, if a,b,c are the side...

In a triangle `ABC`, if `a,b,c` are the sides opposite to angles `A`, `B`, `C` respectively, then the value of `|{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}|` is

A

`1`

B

`-1`

C

`0`

D

`acosA+bcosB+c cosC`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `|{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}|`
Apply `C_(1)toC_(1)+C_(3)` and using projection rule.
`D=|{:(bcosC,a,c cosB+bcosC),(c cosA,b,acosC+c cosA),(acosB,c,bcosA+acosB):}|`
`=|{:(bcosC,a,a),(c cosA,b,b),(acosB,c,c):}|=0`
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