If a = i^ + j^ + k^,b = 4i^ + 

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 Multiple Choice QuestionsMultiple Choice Questions

221.

A girl walks 4 km towards West, then she walks 3 km in a drection 30° East of North and stops. Then, the girl's displacement from herinitial point of departures is

  • - 52i^ + 332j^

  • 12i^ + 32j^

  • - 12i^ + 332j^

  • None of these


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222.

If a = i^ + j^ + k^,b = 4i^ + 3j^ + 4k^ and c = i^ + αj^ + βk^ are linearly dependent vectors and c = 3, then the value of α and β are respectively

  • ± 1, 1

  • ± 2, 1

  • 0, ± 1

  • None of these


A.

± 1, 1

Given, i^ + j^ + k^, 4i^ + 3j^ + 4k^, i^ + αj^ + βk^ are dependent vectors a, b and c are linearly dependent vectors.       a b c = 0 1114341αβ = 0 13β - 4α - 14β - 4 + 14α - 3 = 0 - β + 1 = 0  β = 1Now,                  c = 3 1 + α2 + β2 = 3       1 + 1 + α2 = 3  α2 = 1  α = ± 1                        α = ± 1, 1


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223.

The projection of the vector a = i^ - 2j^ + k^ on  the vextor b = 4i^ - 4j^ + 7k^ is

  • 919

  • 199

  • 9

  • 19


224.

Forces of magnitude 5 and 3 units acting in the directions 6i^ + 2j^ +3k^ and 3i^ - 2j^ +6k^ respectively act on a particle which is displaced from the point (2, 2, - 1) to (4, 3, 1). The work done by the forces is

  • 148 units

  • 1487 units

  • 787 units

  • None of these


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225.

If a and b are unit vectors and θ is the angle between them, then la + bl < 1, if

  • θ = π2

  • θ < π3

  • π  θ > 2π3

  • π3 < θ < 2π3


226.

The points, whose position vectors are 60i + 3j, 40i - 8j and ai - 52j collinear, if

  • a = 40

  • a = - 40

  • a = 20

  • a = - 20


227.

In a ABC, AB = ri + j, AC = si - j if the area of triangle is of unit magnitude, then

  • r - s = 2

  • r + s = 1

  • r + s = 2

  • r - s = 1


228.

If a = i - j + k, a b = 0, a x b = c, where c = - 2i - j + k, then b 1s equal to

  • (1, 0, - 1)

  • (0, 1, 1)

  • (- 1, - 1, 0)

  • (- 1, 0, 1)


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229.

The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then, P2 : Q2 : R2 gven by

  • 2 2 3

  • 3 2 2

  • 2 3 2

  • 2 3 1


230.

Forces ofmagnitudes 3, P, 5, 10 and Q are respectively acting along the sides AB, BC, CD, AD and the diagonal CA of a rectangle ABCD, where AB = 4m and BC = 3m. Ifthe resultant is a single force along the other diagonal BD, then P, Q and the resultant are

  • 4, 10512, 121112

  • 5, 6, 7

  • 312, 8, 912

  • None of the above


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