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If vecaxxvecb = vecbxxvecc ne vec0, prov...

If `vecaxxvecb = vecbxxvecc ne vec0`, prove that `veca+vecc = mvecb`, where m is a scalar.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 8-Section B
  1. Find the vector equation of the plane through the points (2,1, -1) and...

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

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

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

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

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

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  7. Let R be a relation on the set A of ordered pairs of positive integers...

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  8. Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neith...

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  9. If "cos"^(-1)alpha+"cos"^(-1)beta+"cos"^(-1)gamma=3pi, then find alpha...

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  10. Sita and Gita throw a dia alternatively till one of them gets a 6 to w...

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

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  13. Find the points on the curve y = x^3 – 3x^2 + 2x at which the tangents...

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

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

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

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

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

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

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

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