If the vectors 3i^ + j^ - 2k^, i^ +

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291.

If the vectors 3i^ + j^ - 2k^i^ + 2j^ - 3k^3i^ + λj^ + 5k^ are co-planar, the value of λ is

  • - 4

  • 4

  • 8

  • - 8


A.

- 4

Given vectors are,3i^ + j^ - 2k^,i^ + 2j^ - 3k^,3i^ + λj^ + 5k^The vectors are coplanar31- 212- 33λ5 = 0 310 + 3λ - 15 + 9 - 2λ - 6 = 0                30 + 9λ - 14 - 2λ + 12 = 0 7λ + 28 = 0            λ = - 4


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292.

A space vector makes the angles 150° and 60° with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is

  • 90°

  • 60°

  • 180°

  • 120°


293.

If a, b and c are non-coplanar, then the value of a . b × c3b . c × a - b . c × a2c . a × b is

  • - 12

  • - 13

  • - 16

  • 16


294.

If sin-1a is the acute angle between the curves : x2 + y2 = 4x and x2 + y2 = 8 at (2, 2), then a is equal to

  • 1

  • 0

  • 12

  • 32


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295.

The distance of the point P(a, b, c) from the x-axis is

  • a2 + b2

  • b2 + c2

  • a

  • a2 + c2


296.

Equation of the plane perpendicular to the line x1 = y2 = z3 and passing through the point (2, 3, 4) is

  • 2x + 3y + z = 17

  • x + 2y + 3z = 9

  • 3x + 2y + z = 16

  • x + 2y + 3z = 20


297.

The line x - 23 = y - 34 = z - 45 is parallel to the plane

  • 2x + 3y + 4z = 0

  • 3x + 4y + 5z = 7

  • 2x + y - 2z = 0

  • x + y + z = 2


298.

Te angle between two diagonals of a cube is

  • cos-113

  • 30°

  • cos-113

  • 45°


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299.

Lines x - 21 = y - 31 = z - 4- k and x - 1k = y - 42 = z - 51 are coplanar, if

  • k = 2

  • k = 0

  • k = 3

  • k = - 1


300.

If a = i^ + 2j^ + 2k^, b = 5 and the angle between a and b is π6, then the area of the triangle formed by these two vectors as two sides is

  • 154

  • 152

  • 1532

  • 15


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