If a = i^ + j^ + k^, b&nb

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 Multiple Choice QuestionsMultiple Choice Questions

201.

If the vectors a, b and c are coplanar, then

abca . aa . ba . cb . ab . bb . c is equal to

  • 1

  • 0

  • - 1

  • None of these


202.

If the position vectors of the vertices A, B and C are 6i, 6j and k respectively w.r.t. origin 0, then the volume of the tetrahedron OABC is

  • 6

  • 3

  • 16

  • 13


203.

If three vectors 2i - j - k, i + 2j - 3k and 3i + λj + 5k are coplanar, then the value of λ is

  • - 4

  • - 2

  • - 1

  • - 8


204.

The vector perpendicular to the vectors 4i - j + 3k and - 2i + j - 2k whose magnitude is 9

  • 3i + 6j - 6k

  • 3i - 6j + 6k

  • - 3i + 6j + 6k

  • None of the above


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205.

i . j × k + j . k × i + k . j × i is equal to

  • 3

  • 2

  • 1

  • 0


206.

If a = i^ + j^ - 2k^, b = 2i^ - j^ + k^ and c = 3i^ - k^ and c = ma + nb, then m + n is equal to

  • 0

  • 1

  • 2

  • - 1


207.

M and N are the mid-points of the diagonals AC and BO respectively of quadrilateral ABCD, then AB + AD + CB + CD is equal to

  • 2MN

  • 2NM

  • 4MN

  • 4NM


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208.

If a = i^ + j^ + k^b = 2i^ + λj^ + k^c = i^ - j^ + 4k^ and a . b × c = 10, then λ is equal to

  • 6

  • 7

  • 9

  • 10


A.

6

Given, a = i^ + j^ + k^, b = 2i^ + λj^ + k^ and c = i^ - j^ + 4k^Also, given a . b × c = 10 1112λ11- 14 =10 14λ + 1 - 18 - 1 + 1- 2 - λ = 10                          4λ + 1 - 7 - 2 - λ = 10                                                        3λ = 18                                                          λ = 6


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209.

Let PQRS be a quadrilateral. If M and N are the mid-points of the sides PQ and RS respectively, then PS + QR =

  • 3 MN

  • 4 MN

  • 2 MN

  • 2 NM


210.

If vector r with dc's l, m, n is equally inclined to the coordinate axes, then the total number of such vectors is

  • 4

  • 6

  • 8

  • 2


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