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Show that hat(i) xx (vec(a) xx hat(i)) +...

Show that `hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) + hat(k) xx (vec(a) xx hat(k)) = 2 vec(a)`.

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Show that the vectors vec(a) = 3hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) - 3hat(j) + 5hat(k) and vec(c) = 2hat(i) + hat(j) - 4hat(k) form a right angled triangle.

Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

If vec(r) = x hat(i) + y hat(j) + z hat(k) , then find (vec(r) xx hat(i)).(vec(r) xx hat(j)) + xy .

For an vector vec(r) = x hat(i) + y hat(j) + z hat(k) , prove that vec(r) = (vec(r). hat(i))hat(i) + (vec(r).hat(j))hat(j) + (vec(r) .hat(k)) hat(k)

SHARAM PUBLICATION-QUESTION PAPER 2017-EXERCISE
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  2. Solve by Cramer’s rule 2x-y=2, 3x+y=13

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

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

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

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

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

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  8. If a random variable X has a binomial distribution B (8,1/2) then find...

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

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

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  11. Evaluate: int(dx)/(cosx(1+2sinx))

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  12. Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3]

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  13. Prove the following by vector method. An angle inscribed in a semi-cir...

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  14. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

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  15. Show that the line joining the points (0,2,-4) and (-1,1-2) and the l...

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  16. Solve the following LPP graphically : Maximize : Z=5x1+3x2 subject to ...

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

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  18. Show that: C1^2+2C2^2+3C3^2...+nCn^2=frac[(2n-1)!][{(n-1)!}^2

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  19. The probability that a student will pass the final examination in both...

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  20. If P(A) = 0.4, P(B//A) = 0.3 and P(B^(c)/A^(c)) = 0.2. Find P(B).

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