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

Prove that for any three vectors `vec(a), vec(b)` and `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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    MODERN PUBLICATION|Exercise EXERCISE|46 Videos

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For any three vectors vec(a), vec(b) and vec(c) , show that vec(a) - vec(b), vec(b) - vec(c) , vec(c) - vec(a) are coplanar.

For any three vectors vec(a), vec(b) and vec(c) , prove that vec(a) xx (vec(b) - vec(c)) = (vec(a) xx vec(b)) - (vec(a) xx vec(c)) .

Simplify [vec(a)-vec(b)vec(b)-vec(c)vec(c)-vec(a)] .

For any three vectors vec(a), vec(b) and vec(c) , evaluate vec(a) xx (vec(b) + vec(c)) + vec(b) xx (vec(c) + vec(a)) + vec(c) xx (vec(a) + vec(b)) .

Prove that [vec(a)vec(b)vec(c) + vec(d)] = [vec(a)vec(b)vec(c)] + [vec(a) vec(b)vec(d)] .

Prove that the four points with position vectors 2vec(a) + 3vec(b) - vec(c), vec(a) - 2vec(b) + 3vec(c) " , "3vec(a) + 4vec(b) - 2vec(c) and vec(a) - 6vec(b) + 6vec(c) are coplanar.

Prove that vec(a) xx (vec(b) + vec(c)) + vec(b) xx (vec(c) + vec(a)) + vec(c) xx (vec(a) + vec(b)) = vec(0)

MODERN PUBLICATION-SAMPLE PAPER 2018-EXERCISE
  1. Show that int0^1(Inx)/sqrt(1-x^2)dx=pi/2In1/2

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

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  3. From the differential equation whose general solution is y=asint+be^t.

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

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

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  6. Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + ...

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

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

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  9. Two vectors vec A and vec B are inclined to each other at an angle the...

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  10. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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

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  12. Solve the following LPP graphically : Maximize Z=3x(1) +2x(2) subj...

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

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

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

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

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  17. Evaluate: int ((2cosx+7)/(4-sinx))dx

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

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  19. Find the area enclosed by y=4x-1 and y^(2)=2x.

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

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