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If vec a and vec b are two unit vector...

If ` vec a` and ` vec b` are two unit vectors such that ` vec a+ vec b` is also a unit vector, then find the angle between ` vec a` and ` vec bdot`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate : int0^3(dx)/(9+x^2)

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  2. Write the antidervative of (3sqrt(x)+1/(sqrt(x)))dot

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  3. If vec a and vec b are two unit vectors such that vec a+ vec b is a...

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  4. Find the projection of the vector hat i+3 hat j+7 hat k on the vector...

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  5. Show that the lines (x+1)/3=(y+3)/5=(z+5)/7 and (x-2)/1=(y-4)/3=(z-6)/...

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  6. Find the equations of the tangent and normal to the curve x=asin^3t...

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  7. Evaluate : int(pi/6)^(pi/3)(dx)/(1+sqrt(cotx))

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  8. Show that the semi-vertical angle of the cone of the maximum volume an...

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  9. Prove that cot^(-1)((sqrt(1+sin)+sqrt(1-sinx))/(1sqrt(1+sin)-sqrt(1...

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  10. Prove that 2tan^(-1)(1/5)+sec^(-1)((5sqrt(2))/7)+2tan^(-1)(1/8)=pi/4...

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  11. Prove that, for any three vectors vec a , vec b , vec c [ vec a+ v...

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  12. Vector vec a , vec b and vec c are such that vec a+ vec b+ vec c...

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  13. The sum of the perimeters of a circle and a square is k , where k is s...

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  14. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Als...

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  15. Solve for x: 2tan^(-1)(cosx)=tan^(-1)(2cos e cx)

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  16. Using differentials, find the approximate value of (3. 968)^(3/2)

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  17. Write the derivative of sinx w.r.t. cosxdot

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  18. Find : int(sin^2x-cos^2x)/(sin^2xcos^2x)dx

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  19. Write a vector in the direction of the vector hat i-2 hat j+2 hat k t...

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  20. Write the distance of a point P(a ,b ,c) from x-axis.

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