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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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ARIHANT PRAKASHAN-VERY SIMILAR TEST 8-Section B
  1. Sita and Gita throw a dia alternatively till one of them gets a 6 to w...

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  2. If A and B are matrices of the same order and AB=BA, Then prove that ...

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  3. If A(x(1), y(1)), B(x(2), y(2)), and, C(x(3), y(3)) are vertices of an...

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  4. If you throw a pair of dice n times, find the probability of getting a...

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  5. Find the points on the curve y = x^(3) - 3x^(2) + 2x at which the tang...

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  6. Find the interval(s) in which the following functions are (i) increa...

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  7. If sqrt(1-x^4) + sqrt(1-y^4) =k(x^2 - y^2) then show that dy/dx = {x...

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  8. If y=(sinx)^(x)+sin^(-1)sqrt(x), then find (dy)/(dx).

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  9. Examine if Rolle.s theorem is applicable to the function f(x) = cotx o...

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  10. Find the differential equation for the family of curve y= a sin^(-1) x...

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  11. Obtain the general solution of the following differential equations. x...

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  12. Evaluate the following integrals : int((3sinphi-2)cosphi)/(5-cos^(2)...

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  13. Prove that int(0)^(pi//4)2tan^(3)xdx=1-log2.

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  14. Find the area of the region included between the parabola y^(2)=2x and...

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  15. Find the vector equation of the plane through the points (2,1, -1) and...

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  16. Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (...

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  17. If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, wher...

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  18. Find the shortest distance between the lines  (x-3)/(1) = (y - 5)/(-2)...

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  19. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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  20. Corner points of the feasible region determined by the system of linea...

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