Value of a for which the vectors (2, - 1, 1) (1, 2, - 3) and (3,

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 Multiple Choice QuestionsMultiple Choice Questions

351.

The value of k, if the line x - 41 = y - 21 = z - k1 lies on the plane 2x - 4y + z = 7, will be

  • 5

  • 7

  • 9

  • 11


352.

If the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2 = 2 makes angle α with positive direction of x  axis, then cosα will be equal to

  • 12

  • 15

  • 17

  • 13


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353.

Value of a for which the vectors (2, - 1, 1) (1, 2, - 3) and (3, a, 5) become coplanar will be

  • 4

  • - 4

  • no such exists

  • None of these


B.

- 4

Since, given vectors are coplanar, then there exist scalars λ and μ such that 1 + λ + μ = 0 and

12, - 1, 1 + λ1, 2, - 3 + μ2, a, 5 = 0  2 + λ + 3μ = 0[On comparing the coefficients of i^, j^, k^ from both sides]- 1 + 2λ +  = 0    1 - 3λ + 5μ = 0Solving all the three equations, we getλ = - 12, μ = - 12, a = - 4 Option (b) is correct.


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354.

If l , m, n are the DC's of a line, then

  • l2 + m2 + n2 = 0

  • l2 + m2 + n2 = 1

  • l + m + n = 1

  • l = m = n = 1


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355.

The length of the perpendicular from the point (1 2, 3) on the line x - 63 = y - 72 = z - 7- 2 is

  • 3 units

  • 4 units

  • 5 units

  • 7 units


356.

The equation of the plane passing through the intersection ofthe planes 2x - 3y + z - 4 = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0 is

  • x - 5y + 3z - 23 = 0

  • x - 5y - 3z - 23 = 0

  • x + 5y - 3z + 23 = 0

  • x - 5y + 3z + 23 = 0


357.

The angle between the lines x - 23 = y + 1- 2 = z = 2 and x - 11 = y + 33 = z + 52 is

  • cos-1- 3182

  • cos-15182

  • cos-13182

  • cos-1- 5182


358.

If a line makes angles α, β, γ and δ with the four diagonals of a cube, thencos2α + cos2β + cos2γ +cos2δ is

  • 1

  • 2

  • 2/3

  • 4/3


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359.

The angle between the straight lines x + 12 = y - 25 = z + 34 and x - 11 = y + 22 = z - 3- 3 is

  • 45°

  • 30°

  • 60°

  • 90°


360.

The ratio in which the join of (1, - 2,3) and (4, 2, - 1) is divided by the XOY plane is

  • 1 : 3

  • 3 : 1

  • - 1 : 3

  • None of these


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