If the vectors a→ + λb→ +&thins

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181.

If a = b = 1 and a + b = 3, then the value of 3a - 4b . 2a +5b is

  • - 21

  • - 212

  • 21

  • 212


182.

If a is perpendicular to b and ca = 2, b = 3, c = 4 and the angle between b and c is 2π3, then [a b c] is equal to

  • 43

  • 63

  • 123

  • 183


183.

If ab and c are perpendicular to b +cc +a and a +b respectively and if a + b = 6, b + c = 8 and c + a = 10 then a + b + c is equal to

  • 52

  • 50

  • 102

  • 10


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184.

If the vectors a +λb +3c- 2a +3b -4c and a -3b +5c are coplanar, then the value of λ is

  • 2

  • - 1

  • 1

  • - 2


D.

- 2

Since, the given three vectors are coplanar, therefore one of them should be expressible as a linear combination of the remaining two ie, there exist two scalars x and y such that

a +λb +3c = x- 2a +3b -4c + ya -3b +5c

On comparing the coefficient of  a, b and c on both sides, we get

          2x + y = 1 ; 3x - 3y = λ

and - 4x + 5y = 3

On solving first and third equations, we get

x = - 13, y = 13

Since, the vectors are coplanar, therefore these values of x and y, also satisfy the second equation ie, - 1 - 1 = λ

 λ = - 2


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185.

If a + b + c = 0a = 3, b = 5, c = 7, then anle between a and b is

  • π6

  • 2π3

  • 5π3

  • π3


186.

If the vectors a = i^ +aj^ +a2k^b= i^ +bj^ +b2k^ and c = i^ +cj^ +c2k^ are three non-coplanar vectors and aa21 + a3bb21 + b3cc21 + c3 = 0, then the value of abc is

  • 0

  • 1

  • 2

  • - 1


187.

Let a = 2i^ - j^ + k^b = i^ + 2j^ - k^ and c = i^ + j^ - 2k^  be three vectors. A vector in the plane of b and c whose projection on a is magnitude 23, is

  • 2i^ + 3j^ - 3k^

  • 2i^ + 3j^ + 3k^

  • 2i^ - 5j^ + 5k^

  • 2i^ + j^ + 5k^


188.

If the constant forces 2i^ - 5j^ + 6k^ and - i^ + 2j^ - k^act on a particle due to which it is displaced from a point A (4,- 3, - 2) to a point B (6, 1,- 3), then the work done by the forces is

  • 15 unit

  • 9 unit

  • - 15 unit

  • - 9 unit


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189.

If a . i^ = 4, then a × j^ . 2j^ - 3k^ is equal to

  • 12

  • 2

  • 0

  • - 12


190.

a × a × a × b is equal to

  • a × a . b × a

  • a . b × a - ba × b

  • a . a × ba

  • a . a b × a


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