If ABCD is a parallelogram. AB = 2i^ + 4j^ - 

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 Multiple Choice QuestionsMultiple Choice Questions

331.

If (1, 1, 1), (1, - 1, 1), (- 7, - 3, - 5) and (p, 2, 3) are coplanar, then the value of p will be

  • 5

  • 3

  • 2

  • None of these


332.

If u, v, ware three non-coplanar vectors, then (u + v - w){(u - v) x (v - w)} is equal to

  • u . v × w

  • v . u × w

  • w . u × v

  • 0


333.

If the vectros  i^ - 3j^ + 2k^- i^ + 2j^ represents the diagonals ofa parallelogram, then its area will be

  • 21 sq unit

  • 212 sq unit

  • 221 sq unit

  • 214 sq unit


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334.

If ABCD is a parallelogram. AB = 2i^ + 4j^ - 5k^ and AD = i^ + 2j^ + 3k^, then unit vector in the direction of BD is

  • 169i^ + 2j^ - 8k^

  • 169i^ + 2j^ - 8k^

  • 169- i^ - 2j^ + 8k^

  • 169- i^ - 2j^ + 8k^


C.

169- i^ - 2j^ + 8k^

In ABD,

 BD = AD - AB           = i^ + 2j^ + 3k^ - 2i^ + 4j^ - 5k^           = - i^ - 2j^ + 8k^ Unit vector in the direction of BD = BDBD          = - i^ - 2j^ + 8k^1 + 4 + 64          = 169- i^ - 2j^ + 8k^


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335.

The coordinates of foot of perpendicular drawn from the origin on the line formed by joining the points (- 9, 4, 5)and (10, 0, - 1), are

  • (- 3, 2, 1)

  • (1, 2, 2)

  • (4, 5, 3)

  • None of these


336.

If the direction cosines of two lines are represented by l + m + n = 0 and 2lm + 2nl - mn = 0, then the angle between these lines will be

  • π3

  • 2π3

  • π

  • None of these


337.

The direction ratios of the diagonals of a cube which joins the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes)

  • 23, 23, 23

  • 1, 1, 1

  • 2, - 2, 1

  • 1, 2, 3


338.

The equation of the plane in which the lines x - 54 = y - 74 = z + 3- 5 and x - 87 = y - 41 = z - 53 lie, is

  • 17x - 47y - 24z + 172 = 0

  • 17x + 47y - 24z + 172 = 0

  • 17x + 47y + 24z + 172 = 0

  • 17x - 47y + 24z + 172 = 0


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339.

If the lines x - 1- 3 = y - 22k = z - 32 and x - 13k = y - 51 = z - 6- 5 are at right angles, then the value of k will be

  • - 107

  • - 710

  • - 10

  • 7


340.

The coordinates of the point where the line x - 6- 1 = y + 10 = z + 34 meets the plane x + y - z = 3, are

  • (2, 1, 0)

  • (7, - 1, 7)

  • (1, 2, - 6)

  • (5, - 1, 1)


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