Equations of Plane in Different Forms

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  • Q1

    Marks:1
    Answer:

    Explanation:
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  • Q2

    The foot of perpendicular from (a, b, c) on the line x = y = z is the point (r, r, r) where

    Marks:1
    Answer:

    3r = a + b + c.

    Explanation:

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  • Q3

    The equation of the plane which passes through the points (2, 3, –4) and (1, –1, 3) and parallel to x-axis is

    Marks:1
    Answer:

    7y + 4z – 5 = 0.

    Explanation:

    Equation of the plane parallel to x-axis is

    by + cz + d = 0

    Since it passes through the points (2, 3, -4) and (1, -1, 3)

     3b - 4c + d = 0 and -b + 3c + d = 0

     

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  • Q4

    The equation of the plane passing through (1, 0, 0), (0, 1, 0)
    and (0, 0, 1) is

    Marks:1
    Answer:

    x + y + z = 1.

    Explanation:

    Since plane passes through (1, 0, 0), (0, 1, 0) and (0, 0, 1), therefore,

    it makes equal intercepts on x, y and  z-axes, i.e.,1.

    Hence its equation is x/1 +y/1 +z/1 = 1  or x+y+z=1

     

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  • Q5

    The intercept form of the plane x+3y-4z=12 is

    Marks:1
    Answer:

    Explanation:

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