The equation of the plane passing through (2, 3, 4) and parallel

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 Multiple Choice QuestionsMultiple Choice Questions

171.

The point of intersection of the straight lines r = 3i^ - 4j^ + 5k^ + λ- i^ - 2j^ + 2k^ and 3 - x- 1 = y + 42 = z - 57 is

  • (- 3, - 4, - 5)

  • (- 3, 4, 5)

  • (- 3, 4, - 5)

  • (3, - 4, 5)


172.

The vector equation of the straight line x - 2- 1 = y- 3 = 1 - z2 is

  • r = 2i^ + k^ + ti^ + 3j^ + 2k^

  • r = 2i^ - k^ + ti^ - 3j^ - 2k^

  • r = 2i^ + k^ + ti^ - 3j^ + 2k^

  • r = 2i^ + k^ + ti^ - 3j^ - 2k^


173.

The straight line r = (i^ + j^ + 2k^) + t2i^ + 5j^ + 3k^ is parallel to the plane r . (2i^ + j^ - 3k^) = 5. Then, the distance between the straight line and the plane is

  • 914

  • 814

  • 714

  • 614


174.

The distance between (2, 1, 0) and 2x + y + Zz + 5 = 0 is

  • 10

  • 10/3

  • 10/9

  • 5


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175.

The equation of the plane that passes through the points (1, 0, 2), (-1, 1, 2), (5, 0, 3) is

  • x + 2y - 4z + 7 = 0

  • x + 2y - 3z + 7 = 0

  • x - 2y + 4z + 7 = 0

  • 2y - 4z - 7 + x = 0


176.

If a, b, c are vectors such that a + b + c = 0 and a = 7, b = 5, c = 3, then the angle between c and b is

  • π3

  • π6

  • π4

  • π


177.

The angle between the pair of lines x - 22 = y - 15 = z + 3- 3 and x + 2- 1 = y - 48 = z - 54 is

  • cos-121938

  • cos-123938

  • cos-124938

  • cos-126938


178.

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is :

  • 3x + 2y + z + 1 = 0

  • 3x + 2y + z = 0

  • 2x + 3y + z = 0

  • x + y + z = 0


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179.

If 12, 13, n are the direction cosines of a line, then the value of n is

  • 236

  • 2336

  • 23

  • 32


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180.

The equation of the plane passing through (2, 3, 4) and parallel to the plane 5x - 6y + 7z = 3 is :

  • 5x - 6y + 7z + 20 = 0

  • 5x - 6y + 7z - 20 = 0

  • - 5x + 6y - 7z + 3 = 0

  • 5x + 6y + 7z + 3 = 0


B.

5x - 6y + 7z - 20 = 0

Equation of plane parallel to given plane is 5x - 6y + 7z = λ

 It passes through (2, 3, 4) λ = 10 - 18 + 28 = 20 Required equation is 5x - 6y + 7z - 20 = 0 


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