What is the perpendicular distance from the point (2, 3, 4) to th

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If the line x - 41 = y - 21 = z - k2 lies on the plane 2x – 4y + z = 7, then what is the value of k ?

  • 2

  • 3

  • 5

  • 7


22.

A point on the line x - 11 = y - 32 = z + 27 has coordinates

  • (3, 5, 4)

  • (2, 5, 5)

  • ( - 1,  - 1, 5)

  • (2,  - 1, 0)


23.

A point on a line has coordinates p + 1, p - 3, 2p where p is any real number. What are the direction cosines of the line ?

  • 12, 12, 12

  • 12, 12, 12

  • 12, 12, - 12

  • Cannot be determined due to insufficient data


24.

What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane ?

  • x + y = 5

  • z = 5

  • z = 0

  • x + y + z = 5


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25.

Into how many compartments do the coordinate planes divide the space ?

  • 2

  • 4

  • 8

  • 16


26.

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the square of its direction cosines ?

  • (a + b + c)2

  • 2(a + b + c)

  • 3

  • 1


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27.

What is the perpendicular distance from the point (2, 3, 4) to the line x - 01 = y - 00 = z - 00 ?

  • 6 units

  • 5 units

  • 3 units

  • 2


B.

5 units

Coordinate of general point on x - 01 = y - 00 = z - 00 = λi.e. x = λ, y = 0, z = 0Let the coordinate of L be λ, 0, 0Direction ratio of PL areλ - 2, - 3, - 4Direction of given lines are 1, 0, 0Since PL is perpendicular to the given line 1λ - 2 + 0 - 3 +0- 4 = 0   λ = 2, L = 2, 0, 0PL = 2 - 22 + 0 + 32 +0 + 42 = 25 = 5 units


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28.

What is the length of the diameter of the sphere whose centre is at (1, 2, 3) and which touches the plane 6x – 3y + 2z – 4 = 0 ?

  • 1 unit

  • 2 units

  • 3 units

  • 4 units


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