The distance between the line r→ = 2i^ -

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 Multiple Choice QuestionsMultiple Choice Questions

51.

For any three vectors a, b and c [a + b, b + c, c + a] is

  • [a, b, c]

  • 3[a, b, c]

  • 2[a, b, c]

  • 0


52.

If r = αb × c + βc × a + γa × b and [a b c] = 2, then α + β + γ is equal to

  • r . b × c + c × a + a × b

  • 12r . a +b + c

  • 2r . (a + b + c)

  • 4


53.

If a, b, c are three non-coplanar vectors and p, q, rare reciprocal vectors, then (la + mb + nc) · (lp + mq + nr) is equal to

  • l + m + n

  • l3 + m3 + n3

  • l2 + m2 + n2

  • None of these


54.

The vector b = 3j + 4k is to be written as the sum of a vector b1 parallel to a = i + j and a vector b2 perpendicular to a. Then, b1 is equal to

  • 32(i + j)

  • 23(i + J)

  • 12(i + j)

  • 13(i + j)


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55.

If a = i + j + k, b = i + 3j + 5k and c = 7i + 9j + 11k, then the area of parallelogram having diagonals a + b and  b + c is

  • 46 sq units

  • 1221 sq units

  • 62 sq units

  • 6 sq units


56.

The projection of the vector i - 2j + k on the vector 4i - 4j + 7k is

  • 5610

  • 199

  • 919

  • 619


57.

If a, b, c are three non-zero vectors such that a + b+ c = 0 and m = a . b + b . c + c · a, then

  • m < 0

  • m > 0

  • m = 0

  • m = 3


58.

If a = 2i^ + 2j^ + 3k^b = - i^ + 2j^ + k^ and c = 3i^ + j^ then a + tb is perpendicular to c, if t is equal to

  • 2

  • 4

  • 6

  • 8


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59.

The distance between the line r = 2i^ - 2j^ + 3k^ + λi^ - j^ + 4k^ and the plane r .  i^ + 5j^ + k^ = 5, is

  • 103

  • 103

  • 1033

  • 109


C.

1033

We have the given line

r = 2i^ - 2j^ + 3k^ + λi^ - j^ + 4k^On comparing it with r = a + tb, we geta = 2i^ - 2j^ + 3k^, b = i^ - j^ + 4k^Also, the plane isr . i^ + 5j^ + k^  = 5On comparing it with r . n = d, we getn = i^ + 5j^ + k^ and d = 5Since, b . n = i^ - j^ + 4k^ . i^ + 5j^ + k^                       = 1 - 5 + 4 = 0  Given line is parallel to the given plane.

Now, distance between the line and the plane 1s given by required distance = a . n - dn

= 2i^ - 2j^ + 3k^ . i^ + 5j^ + k^1 + 25 + 1= 2 - 10 + 3 - 527 = 1033


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60.

If m1, m2, m3 and m4 are respectively the magnitudes of the vectors

a1 = 2i^ - j^ + k^, a2 = 3i^ - 4j^ - 4k^,a3 = i^ + j^ - k^ and a4 = - i^ + 3j^ + k^,

then the correct order of m1, m2, m3 and m4 is

  • m3 < m1 < m4 < m2

  • m3 < m1 < m2 < m4

  • m3 < m4 < m1 < m2

  • m3 < m4 < m2 < m1


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