The Planes — Practice Quiz
Telangana Open School (TOSS) · Class 12 · Mathematics
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Quick Quiz: The Planes
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Which of the following represents the general equation of a plane?
How many constants are there in the general equation of a plane?
The equation of a plane passing through the origin is of the form:
The intercept form of the equation of a plane is:
Sample Questions
If a plane makes equal intercepts on the coordinate axes, then its equation can be written as:
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x + y + z = a
If intercepts are equal, say a, then the equation is x/a + y/a + z/a = 1, which simplifies to x + y + z = a.
The normal form of the equation of a plane is:
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lx + my + nz = p
In the normal form, l, m, n are the direction cosines of the normal to the plane, and p is the length of the perpendicular from the origin.
The direction cosines of the normal to the plane 2x + 3y + 6z = 7 are proportional to:
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2, 3, 6
For the plane ax + by + cz + d = 0, the direction ratios of the normal are a, b, c. So here they are 2, 3, 6.
The length of the perpendicular from the origin to the plane 3x + 4y + 12z = 5 is:
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5/13
The length is |d| / √(a² + b² + c²) = |5| / √(3² + 4² + 12²) = 5 / √(9+16+144) = 5/√169 = 5/13.
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