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If a ,\ b ,\ c are real numbers such t...

If `a ,\ b ,\ c` are real numbers such that `|(b+c,c+a ,a+b),( c+a,a+b,b+c),(a+b,b+c,c+a)|=0` , then show that either `a+b+c=0` or, `a=b=c` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
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  2. Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 whe...

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  3. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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  4. a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-...

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  5. Show that x=2 is a root of the equation |(x,-6,-1),( 2,-3x,x-3),(-3,...

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  6. Solve the following determinant equation: |[x+a, b, c], [c, x+b, a],...

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  7. Solve the following: |[x+1, 3, 5], [2,x+2, 5], [2, 3,x+4]|=0

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  8. Solve the following: |[1, 1,x], [p+1,p+1,p+x],[3,x+1,x+2]|=0

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  9. If a ,b and c are all non-zero and |(1+a,1,1),( 1,1+b,1),(1,1,1+c)|=...

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  10. Find the area of the triangle with vertices A\ (5,\ 4),\ \ B(-2,\ 4...

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  11. Show that pointsA (a , b + c), B (b , c + a), C (c , a + b)are collin...

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  12. If the points (a1, b1),\ \ (a2, b2) and (a1+a2,\ b1+b2) are collinear,...

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  13. If the points (2,\ -3),\ (lambda,\ -1) and (0,\ 4) are collinear, find...

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  14. Using determinants, find the area of the triangle whose vertices ar...

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  15. Find the equation of the line joining A(1,\ 3) and B(0,\ 0) using d...

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  16. If A(x1, y1),B(x2, y2)a n dC(x3,y3) are vertices of an equilateral tri...

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  17. A triangle has its three sides equal to a , ba n dc . If the coordinat...

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  18. Find the area of the triangle with vertices at the points: (3, 8), ...

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  19. Find the area of the triangle with vertices at the points: (0, 0), ...

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  20. Using determinants show that the following points are collinear: (1...

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