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Prove that, for any three vectors vec a...

Prove that, for any three vectors ` vec a , vec b ,` ` vec c` `[ vec a+ vec b , vec b+ vec c , vec c+ vec a]=2[ vec a , vec b , vec c]`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Prove that cot^(-1)((sqrt(1+sin)+sqrt(1-sinx))/(1sqrt(1+sin)-sqrt(1...

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

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

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

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

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

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

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

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

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

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

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

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  13. If, [xdoty4z+6x+y]=[8w0 6], write the value of (x+y+z)dot

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  14. Write the principal value of cos^(-1)[cos(680^@)]

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  15. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

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  16. Write a x2x matrix which is both symmetric and skew-symmetric.

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  17. Write the projection of the vector 2 hat i- hat j+ hat k on the vector...

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  18. int[x+3]/sqrt[5-4x-x^2].dx

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  19. Evaluate : int0^(pi/2)x^2sinxdx

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  20. If the three vectors veca, vecb , vecc are coplanar, prove that the ve...

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