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With the usual notation in DeltaABC det|...

With the usual notation in `DeltaABC` det`|(1,1,1),(sinA,sinB,sinC),(sin^(2)A,sin^(2)B,sin^(2)C)|` assumes the value

A

`(1)/(8R^(3))(a-b)(b-c)(c-a)`

B

`(a-b)(b-c)(c-a)`

C

`(1)/(8R)(a-b)(a-c)(b-c)`

D

`8R^(3)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
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  2. If |{:(0,sinalpha,sinbeta),(sinalpha,0,singamma),(sinbeta,singamma,0):...

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  3. With the usual notation in DeltaABC det|(1,1,1),(sinA,sinB,sinC),(sin^...

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  4. If y=cosx,y(n)=(d^(n)(cosx))/(dx^(n)) then |{:(y(4),y(5),y(6)),(y(7),y...

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  5. If |{:(cos(A+B),-sin(A+B),cos2B),(sinA,cosA,sinB),(-cosA,sinA,cosB):}|...

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  6. A=[(1, cos (beta-alpha),cos(gamma-alpha)),(cos (alpha-beta), 1, cos(ga...

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  7. If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(...

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  8. If a!=p,b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 then the value of P/...

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  9. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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  10. A and B be 3xx3 martrices. Then AB=0 implies

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  11. If x,y,z are in A.P. then the value of |{:(a+2,a+3,a+3x),(a+3,a+4,a+2y...

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  12. |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(2))|=0,x!=y!=zimpli...

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  13. If f(x)=|(2cosx,1,0),(x-pi//2,2cosx,1),(0,1,2cosx)| then (df)/(dx) at ...

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  14. If Delta(1)=|(x,b,b),(a,x,b),(a,a,x)|, Delta(2)=|(x,b),(a,x)| then

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  15. Statment - I : |{:(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0...

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  16. Arrange the following matrices in ascending order of their determinant...

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  17. Match the following from List - I to List - II {:("List-I","List-II"...

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  18. Assertion (A) : |{:(0,p-e,e-r),(e-p,0,r-p),(r-e,p-r,0):}|=0 Reason ...

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  19. |{:(2013^(2),2014^(2),2015^(2)),(2016^(2),2017^(2),2018^(2)),(2019^(2)...

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  20. If ainR then |{:(a^(2),(a+1)^(2),(a+2)^(2)),((a+1)^(2),(a+2)^(2),(a+3)...

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