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Prove that the vectors 2hati-hatj+hatk, ...

Prove that the vectors `2hati-hatj+hatk`, `hati-3hatj-5hatk`, `3hati-4hatj-4hatk` are the sides of a right angled triangle.

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Find the value of 'a' do the which the pointA,B,C with position vectors 2hati-hatj+hatk,hati-3hatj-5hatk and ahati-3hatj+hatk respectively are the vertices of a right angled triangle with /_C=pi/2 .

Show that the vectors 4hati+4hatj+ 4hatk,7hati+6hatj-hatk and 3hati+2hatj-5hatk form a right angled triangle and find its area.

Show that the vectors 2hati + 3hatj,5hati -5hatk and 6hatj + 4hatk are co-planar.

Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+4hatj+5hatk, -2hati+4hatj-4hatk .

Prove that four points with position vectors hati+hatj-3hatk, 2hati -hatj-hatk,- hati +2hatj +2hatk and 2hati +2hatk arecoplanar

Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati-4hatj+5hatk, 3hati+6hatj+hatk

Find the angle between the vectors 3hati+ 4hatj and 2hati+hatj+hatk .

If veca = hati+2hatj-hatk , vecb = hati+hatj+2hatk , vecc = 2hati-hatj then

If the vectors hati+2hatj+hatk & 2hati+3hatj+alphahatk are perpendicular, find alpha

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2017-PREVIOUS YEAR QUESTION
  1. Solve the following differential equation (x+2y^(3))dy/dx=y.

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  2. Solve the following second order equations cosec x(d^(2)y)/(dx^2)=x

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  3. Prove that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk, 3hati-4hatj-...

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  4. If veca=3hati+hatj+2hatk,vecb=2hati-3hatj+4hatk then verify that vecat...

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  5. If vecp=frac[1][lambda](vecbtimesvecc),vecq=frac[1][lambda](vecctimes...

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  6. Find the equation of the plane through the point (2,1,0) and passing t...

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  7. Find the co-ordinates of the point where the perpendicular from the or...

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  8. Find the value of a for which the plane x+y+z-a=0 will touch the spher...

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  9. Find the feasible region of the system. 2y-xge0,6y-3xle21,xge0,yge0

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  10. Solve the following LPP graphically: Maximize z=20x+30y subject to 3x+...

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  11. Solve by Cramer’s rule 2x-y=2, 3x+y=13

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  12. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  13. Find the inverse of the following matrix: [[0,0,2],[0,2,0],[2,0,0]]

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  14. If P(n-1,3):P(n+1,3)=5:12, find n.

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  15. A cricket team consisting of 11 players is to be chosen from 8 batsmen...

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  16. Write the principal value of sin^(-1)frac[1][2]+cos^(-1)(-frac[1][2])

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  17. Five boys and four girls randomly stand in a line. Find the probabilit...

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  18. If a random variable X has a binomial distribution B(8,frac[1][2]), th...

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  19. If (a + bx)e^(y/x) = x, then show that x^3d/dx (dy/dx) = (x dy/dx - ...

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  20. A cylindrical open water tank with a circular base is to be made out o...

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