Let u = i^ + j^, v = i^ - j^ and w = i^ 

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 Multiple Choice QuestionsMultiple Choice Questions

351.

If the vectors c, a = xi^ + yj^ + zk^ and b = j^ are such that a, c and b form a right handed system, then c is

  • zi^ - xk^

  • 0

  • yj^

  • - zi^ + xk^


352.

The vector i^ + xj^ + 3k^ is rotated through an angle θ and doubled in magnitude, then it becomes 4i^ + 4x - 2j^ + 2k^. Then, the values of x are

  • - 23, 2

  • 13, 2

  • 23, 0

  • 2, 7


353.

If a = (1, - 1) and b = (- 2, m) are two collinear vectors, then m is equal to

  • 4

  • 3

  • 2

  • 0


354.

For any vector a i^ × a × i^ + j^ × a × j^ + k^ × a × k^ is equal to

  • 2a

  • 3a

  • - 2a

  • a


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355.

If the a, band c form the sides BC, CA and AB respectively, of a ABC, then

  • a . b + b . c + c . a = 0

  • a × b = b × c = c × a

  • a . b = b . c = c . a = 0

  • a × b + b × c + c × a


356.

If a, b and c are three vectors, such that a + b + c = 0a = 1, b = 2, c = 3, then a . b + b . c + c . a is equal to

  • 0

  • - 7

  • 7

  • 1


357.

If the position vectors of P and Q are i^ + 3j^ - 7k^ and 5i^ - 2j^ + 4k^, then PQ is

  • 158

  • 160

  • 161

  • 162


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358.

Let u = i^ + j^, v = i^ - j^ and w = i^ + 2j^ + 3k^. If n^ is a unit vector such that u . n^ = 0 and v . n^ = 0, then w . n^ is equal to

  • 0

  • 1

  • 2

  • 3


D.

3

Given, u = i^ + j^, v = i^ - j^ and w = i^ + 2j^ + 3k^Also, u . n^ = 0 and v . n^ = 0 n^ is a unit vector perpendicular to u and v. n = u × vu × v = i^ + j^ × i^ - j^i^ + j^ × i^ -+ j^ = - k^w . n^ = i^ + 2j^ + 3k^ . - k^         = - 3 w . n^ = - 3 = 3


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359.

If A = i^ - 2j^ - 3k^, B = 2i^ + j^ - k^ and C = i^ + 3j^ - 2k^, then A × B × C is

  • 5- i^ + 3j^ + 4k^

  • 4- i^ + 3j^ + 4k^

  • 5- i^ - 3j^ - 4k^

  • 4i^ + 3j^ + 4k^


360.

A particle is acted upon by constant forces 4i^ + j^ - 3k^ and 3i^ + j^ - k^ which displace it from a point i^ + 2j^ + 3k^ to the point 5i^ + 4j^ + k^. The work done in standard unit by the forces is given by

  • 40

  • 30

  • 25

  • 15


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