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If A(x(1), y(1)), B(x(2), y(2)), and, C(...

If `A(x_(1), y_(1)), B(x_(2), y_(2))`, and, `C(x_(3), y_(3))` are vertices of an equilateral triangle whose each side is equal to a, then prove that `|(x_(1), y_(1), 2),(x_(2), y_(2), 2),(x_(3), y_(3), 2)|^(2) = 3a^(4)`.

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`=3a^(4)`
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ARIHANT PRAKASHAN-VERY SIMILAR TEST 2 -SECTION -B
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  4. A random variable X has following probability distribution . Fin...

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  5. A random variable X has following probability distribution . Fin...

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  6. A random variable X has following probability distribution . Fin...

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  7. A random variable X has following probability distribution . Fin...

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  8. If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t)), then show that (dy)/(d...

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  9. Find the extreme points of the function f(x)=x^(2)sqrt(1-x^(2)). Als...

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  10. Verify the LMVT for the function f(x)=(1)/(4x-1),1lexle4.

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  11. Using differentials, find approximate value (255)^(1//4)

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  12. Find the equations of all lines having slope -1, that are tangent to t...

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  13. Evaluate int(1)/(sqrt(8+3x-x^(2)))dx.

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  14. Evaluate int(0)^(pi//4)tan^(5)xdx.

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  15. Find the area enclosed by the ellipse (x^(2))/(16)+(y^(2))/(9)=1.

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  16. Form the differential equation of the family of circles having centr...

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  17. If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(...

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  18. If veca,vecb and vecc are three vectors such that |veca|=5,|vecb|=12,|...

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  19. If veca,vecb are unit vectors such that the vector veca+3vecb is per...

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