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If a,b and c are complex numbers the de...

If a,b and c are complex numbers the determinant
`Delta|{:(0,-b,-c),( overset-b,0,-a),(overset-c,overset-a,0):}|` is

A

a non-zero real number

B

purely imaginary

C

0

D

None of these

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If a, b, c are complex numbers, then the determinant Delta = |(0,-b,-c),(bar(b),0,-a),(bar(c),bar(a),0)| , is

If four points A (overset(-)a), B(overset(-)b), C (overset(-)c) & D(overset(-)d) are coplanar then show that [ overset (-)a overset (-)b overset(-)d ]+ [ overset (-) b overset (-)c overset (-)d ]+ [ overset (-) c overset (-)a overset (-)d ]= [overset (-)a overset (-)b overset (-)c ]

If vectors overset(to)(a) , overset(to)(b) , overset(to)( C) are coplanar then show that |{:(overset(to)(a),,overset(to)(b),,overset(to)(c )),(overset(to)(a)"."overset(to)(a),,overset(to)(a)"."overset(to)(b),,overset(to)(a)"."overset(to)(c )),(overset(to)(b)"."overset(to)(a),,overset(to)(b)"."overset(to)(b),,overset(to)(b)"." overset(to)(c )):}|

Let overset(rarr)C = overset(rarr)A+overset(rarr)B then :

Let the vectors overset(to)(a), overset(to)(b), overset(to)( c) " and " overset(to)(d) be such that (overset(to)(a) xx overset(to)(b)) xx ( overset(to)(c ) xx overset(to)(d)) = overset(to)(0) . " If " P_(1) " and " P_(2) are planes determined by the pairs of vectors overset(to)(a) , overset(to)(b) " and " oerset(to)(c ) , overset(to)(d) respectively then the angle between P_(1) " and "P_(2) is

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

If the vectors overset(to)(b), overset(to)(c ) , overset(to)(d) are not coplanar then prove than the vectors (overset(to)(a) xx overset(to)(b)) xx (overset(to)(c ) xx overset(to)(d)) + (overset(to)(a) xx overset(to)(c )) xx (overset(to)(d) xx overset(to)(b)) +(overset(to)(a) xx overset(to)(d)) xx (overset(to)(b) xx overset(to)( c)) is parallel to overset(to)(a)

A,B,C and d are four points in a plane with position vectors overset(to)(a),overset(to)(b),overset(to)(c ) and overset(to)(d) respectively such that (overset(to)(a)-overset(to)(d)).(overset(to)(b)-overset(to)(c))=(overset(to)(b)-overset(to)(d))(overset(to)(c)-overset(to)(a))=0 The point D then is the .... of the DeltaABC

If overset(to)(a) , overset(to)(b) , overset(to)(c ) are non-coplanar unit vectors such that overset(to)(a) xx (overset(to)(b) xx overset(to)(c )) = ((overset(to)(b) + overset(to)(c )))/(sqrt(2)) , then the angle between overset(to)(a) " and " overset(to)(b) is

if overset(to)(a),overset(to)(b) " and " overset(to)(c ) are unit vectors then |overset(to)(a)-overset(to)(b)|^(2)+|overset(to)(b)-overset(to)c|^(2)+|overset(to)(c)-overset(to)(a)|^(2) does not exceed

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a,b and c are complex numbers the determinant Delta|{:(0,-b,-c),...

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  2. If a^(2)+b^(2)+c^(2)=-2 and f(x)= |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x...

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  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

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  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

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  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

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  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  11. If the trivial solution is the only solution of the system of equation...

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  12. The number of values of k, for which the system of equations (k""+"...

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  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

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  14. The set of the all values of lamda for which the system of linear equa...

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  15. Which of the following values of alpha satisfying the equation |(1+alp...

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  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

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  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

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  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

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  19. If S is the set of distinct values of ' b for which the following syst...

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