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Prove that the lines joining the midpoin...

Prove that the lines joining the midpoints of consecutive sides of a quadrilateral form a parallelogram using vector method.

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Prove by vector method that the lines joining the mid points of consecutive sides of a quadrilateral is a parallelogram.

Prove by vector method that the line segment joining the mid points of two sides of a triangle is parallel to the third and half of it.

Prove analytically : The line segment joining the midpoints of two sides of a triangle is parallel to the third and half of its length.

Prove by vector method that the diagonals of a quadrilateral bisect each other iff is a parallelogram.

Prove by vector method that the diagonals of a parallelogram bisect each other.

Prove that magnitude of cross product of two vectors is equal to the area of the parallelogram with those two sides as vectors.

Prove that the sum of the vectors directed from the vertices to the mid points of opposite sides of a triangle is zero

Prove by vector method that in a parallelogram, the line joining a vertex to the midpoint of an oppositeside trisects the other diagonal.

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MODERN PUBLICATION-SAMPLE PAPER 2015-EXERCISE
  1. Solve the following differential equation (x+2y^(3))dy/dx=y.

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  2. Solve the following differential equation : x^(2)(y-1)dx+y^(2)(x-1)dy ...

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  3. Prove that the lines joining the midpoints of consecutive sides of a q...

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  4. Prove that : [(vec a × vec b) (vec b × vec c) (vec c × vec a)] = [vec ...

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  5. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

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

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  7. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  8. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  9. Solve the following LPP graphically : Minimize Z = 6x(1)+7x(2) Sub...

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  10. Find the feasible region the the following system of equations 2y-xge0...

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  11. Solve the following equations by cramer's rule : 7x+y+1 = 0, x+13y+5 =...

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  12. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  13. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  14. How many four digits even numbers with distict digits can be formed ou...

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  15. In how many ways can 10 boys and 10 girls sit in a row so that no two ...

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  16. Find the fifth term in the expansion of (6x-a^3/x)^10

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  17. Two different digits are selected at random from the digits 1 through ...

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  18. Suppose that the probability that your alarm goes off in the morning i...

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  19. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  20. Evaluate intfrac[dx][cosx(1+2sinx)]

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