If θ is the angle between the lines AB and AC where A, B an

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 Multiple Choice QuestionsMultiple Choice Questions

81.

If A(- 2, 1), B(2, 3) and C( - 2, - 4) are three points. Then the angle between BA and BC is

  • tan-123

  • tan-132

  • tan-113

  • tan-112


82.

In a ABCa + b + cb + c - ac + a - ba + b - c4b2c2 equals

  • cos2A

  • cos2B

  • sin2A

  • sin2B


83.

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0, l2 + m2 - n2 = 0 is

  • π6

  • π4

  • π3

  • π2


84.

The plane through the point (- 1, - 1, - 1) and containing the line of intersection of the planes r . i^ + 3j^ - k^ = 0 and r . j^ + 2k^ = 0 is

  • r . i^ + 2j^ - 3k^

  • r . i^ + 4j^ + k^

  • r . i^ + 5j^ - 5k^

  • r . i^ + j^ + 3k^


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85.

If θ is the angle between the lines AB and AC where A, B and C are the three points with coordinates (1, 2, - 1), (2, 0, 3), (3, - 1, 2) respectively, then 462 cosθ is equal to

  • 20

  • 10

  • 30

  • 40


A.

20

Since, the coordinates of A, B and C are (1, 2, - 1), (2, 0, 3), (3, - 1, 2), then

       AB = 2 - 1i^ + 0 - 2j^ + 3 + 1k^             = i^ - 2j^ + 4k^and AC = 3 - 1i^ + - 1 - 2j^ + 2 + 1k^             = 2i^ - 3j^ + 3k^cosθ = i^ - 2j^ + 4k^ . 2i^ - 3j^ + 3k^1 + 4 + 16 4 + 9 + 9          = 2 + 6 + 122122 = 20462            462cosθ = 20


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86.

Let the pairs a, b and c, d each determine a plane. Then the planes are parallel, if :

  • a × c and b × d = 0

  • a × c . b × d = 0

  • a × b × c × d = 0

  • a × b . c × d = 0


87.

The area of a parallelogram with 3i^ + j^ - 2k^ and i^ - 3j^ + 4k^ as diagonal is :

  • 72

  • 73

  • 74

  • 75


88.

In a ABC, if 3 - 1a = 2b, A = 3B, then C is

  • 60°

  • 120°

  • 30°

  • 45°


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89.

The x - axis, y - axis and a line passing through the point A (6, 0) from a ABC. If A = 30°, then the area of the , in sq unit is

  • 63

  • 123

  • 43

  • 83


90.

The mid point of the line joining the points (- 10, 8) and (- 6, 12)divides the line joining the points ( 4, - 2) and (- 2, 4) in the ratio

  • 1 : 2 internally

  • 1 : 2 externally

  • 2 : 1 internally

  • 2 : 1 externally


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