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Prove the following: |[ax-by-cz,ay+bx,...

Prove the following:
`|[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],[cx+az,ay+bz,cz-ax-by]|`
=`(a^2+b^2+c^2)(ax+by+cz)(x^2+y^2+z^2)`

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MODERN PUBLICATION-TEST PAPER 5-PROBLEM
  1. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  2. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  3. Evaluate int0^2abs(x^2+2x-3)dx

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  4. solve:ydx-xdy=xydx

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  5. int(xe^x)/(1+x^2)dx

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  6. int0^pi(xdx)/(1+sinx)

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  7. Solve : (x + 2y^3)dy/dx = y.

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  8. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  9. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  10. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  11. Find the direction cosines of the line which is perpendicular to the l...

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  12. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  13. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  14. Exaniming consistency and solvability, solve the following equations b...

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  15. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

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  16. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  17. Show that the semi-vertical angle of a right circular cone of minimum ...

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  18. int0 ^pi (( tan x) / (sinx +tan x))dx

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  19. Find the area of the regions into which the circle x^2+y^2=4 is divide...

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  20. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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