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If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+...

If `a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f,` then prove that `|(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  3. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

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  4. If A , B ,a n dC are the angles of triangle, show that the system of...

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  5. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  8. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

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  9. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

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  10. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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  11. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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  12. The product of all values of t , for which the system of equations (a-...

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  13. "If " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fol...

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  14. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

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  15. Factorize: a x+b x+a y+b y +a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+...

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  16. If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...

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  17. The sum of values of p for which the equations x+y+z=1, x+2y +4z...

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  18. The value of |alpha| for which the system of equation alphax+y+z=...

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  19. Let D1=|[a, b, a+b], [c, d, c+d], [a, b, a-b]| and D2=|[a, c, a+c], [b...

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  20. Three distinct points P(3u^(2),2u^(3));Q(3v^(2),2v^(3)) and R(3w^(2),2...

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