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Prove that when the sides of a triagle a...

Prove that when the sides of a triagle are taken in order, it leads to zero resultant.

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Assertion: The minimum number of vectors of unequal magnitude required to produce zero resultant is three. Reason: Three vectors of unequal magnitude which can be represented by the three sides of a triangle taken in order, produce zero resultant.

If vec a ,\ vec b ,\ vec c be the vectors represented by the sides of a triangle, taken in order, then prove that vec a+ vec b+ vec c= vec0dot

If vec a ,\ vec b ,\ vec c\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only, if

If A,B,C represents the three sides of an equilateral triangle taken in the same order then find the angle between i) A and B ii) B and C iii) A and C.

Using vector method, prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral taken in order form a parallelogram.

If the mid-points of the sides of a quadrilateral are joined in order, prove that the area of the parallelogram, so formed will be half of the area of the given quadrilateral (figure).

Let A_1 A_2 A_3 A_4 A_5 A_6 A_1 be a regular hexagon. Write the x-components of the vectors representeed by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that cos0+cospi/3+cos(2pi)/3+cos(4pi)/3+cos(5pi)/3=0 Use the known cosine values of verify the result. .

AAKASH SERIES-ELEMENTS OF VECTORS-NUMERICAL EXXERCISE (LEVEL -2)
  1. Two vectors of equal magnitude have a resultant equal to either of the...

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  2. A force (2hati+3hatj-hatk) newtons acts on a particle having position...

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  3. A body of mass 10 kg is suspended by a string and is pulled a side wit...

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  4. A man is travelling at 10.8 kmph in a topless car on a rainy day. He h...

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  5. A body starts with a velocity 2 hati +3hatj +11 hatk m/s and moves wi...

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  6. Prove that when the sides of a triagle are taken in order, it leads to...

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  7. Resultant of two vector of equal magnitude A is

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  8. A vector makes angle with X,Y and Z axer that are in the ratio 1:2:1 r...

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  9. The components of a particles velocity in the directions at right angl...

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  10. Two vectors vecP and vecQ are having their magnitudes in the ratio s...

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  11. A vector makes angles alpha,beta "and" gamma with the X,Y and Z axes r...

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  12. At a given instant of time two particles are having the position vecto...

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  13. IF barP + barQ = barR and P=Q = (R )/(sqrt(2)) then find the a...

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  14. The sum of the magnitudes of wto forces acting at a point is 18 and th...

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  15. Two particles A And B , move with constant velocities v(1) and v(2) At...

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  16. A launch plies between two points A and B on the opposite banks of a r...

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  17. A boat moves perpendicular to the bank with a velocity of 7.2 km/h. Th...

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  18. An aeroplane is flying with a velocity 800kmph relative to air wind is...

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  19. A swimmer is capable of swimming at 1.65ms- in still water. If he swim...

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  20. A boat moves relative to water with a velocity with a velocity v is n ...

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