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Prove the following by vector method. Th...

Prove the following by vector method. The diagonals of a rhombus are at right angles.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
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  2. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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  3. Prove the following by vector method. The diagonals of a rhombus are a...

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  4. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

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  5. int0^pi((xtanx)/(secx+tanx))dx

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  6. Solve: (1+x^2)dy/dx+2xy-x^3=0

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  7. Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2

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  8. If x cos alpha + y sin alpha = p is a tangent to the curve (x/a)^(n/...

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  9. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  10. If A=[(0,1,0),(-1,0,2),(0,0,1)], then show that A^3-A^2+I3=[(2,-1,0),(...

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  11. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  12. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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  13. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  14. A line makes angles alpha, beta, gamma, delta with the four main diago...

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  15. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  16. The equation of a plane passing through (1, 1, 2) and parallel to x + ...

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  17. What is the value of int0^100[tan^(-1)x]dx ?

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  18. What is the trigonometric function f(x) such that f''(x)+f(x)=0?

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  19. Write whether the following statements are true or false. "sec"^(-1)...

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  20. What is the minimum value of |[sin x ,cosx], [-cosx, 1+ sinx]|?

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