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If the position vectors of two points A and B are `3hati + hatk` and `2hati+hatj-hatk`, then the vector `vec(BA)` is

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The position vectors of two points A and B are 3hati+hatj+2hatk and hati-2hatj-4hatk , respectively. Find the equation of the plane passing through B and prependicular to AB.

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

Write a vector normal to hati+hatk and hati+hatj .

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 .

Find the angle between the vectors 3hati + 4hatj and 2hati+hatj+sqrt3hatk

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

The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and hati-2hatj-3hatk . Find the unit vector parallel to its diagonal. Also find its area.

Find the unit vectors perpendicular to the vectors. 2hati-3hatj+hatk , -hati+2hatj-hatk .

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2018-PREVIOUS YEAR QUESTION
  1. From the differential equation whose general solution is y=asint+be^t.

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  2. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  3. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  4. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  5. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  6. Prove that the measure of the angle between two main diagonals of a cu...

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  7. If the position vectors of two points A and B are 3hati + hatk and 2ha...

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  8. If A and B are invertible matrices of the same order, then prove that ...

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  9. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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  10. Solve the following LPP graphically: Maximize Z=3x1+2x2, x1le2, x1+x2l...

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  11. Solve the following system of equations by the matrix inversion method...

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  12. Two cards are drawn successively with replacement from a well-shuffled...

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  13. By elementary operations, find A^(-1) for the following: A=[[1,1,0],[1...

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  14. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  15. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

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  16. Evaluate intfrac[2cosx+7][4-sinx]dx

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  17. Find the solution of the following differential equations: (4x+6y+5)dx...

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  18. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  19. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

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