Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 29

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An equation of a plane parallel to the plane $x - 2 y + 2 z - 5 = 0$ and at a unit distance from the origin is

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Important Questions on Three Dimensional Geometry

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 30

If the line

\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}

and

\frac{x - 3}{1} = \frac{y - k}{2} = \frac{z}{1}

intersect, then

k

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 31

Distance between two parallel planes

2 x + y + 2 z = 8

and

4 x + 2 y + 4 z + 5 = 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 32

If the lines

\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}

and

\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}

are coplanar, then

k

can have

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 33

The image of the line

\frac{x - 1}{3} = \frac{y - 3}{1} = \frac{z - 4}{- 5}

in the plane

2 x - y + z + 3 = 0

is the line

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 34

The angle between the lines whose direction cosines satisfy the equations

l + m + n = 0

and

l^{2} = m^{2} + n^{2}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 35

The distance of the point

(1, 0, 2)

from the point of intersection of the line

\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}

and the plane

x - y + z = 16,

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 36

The equation of the plane containing the line

2 x - 5 y + z = 3, x + y + 4 z = 5

and parallel to the plane

x + 3 y + 7 z = 1,

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 37

If the line,

\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}

lies in the plane,

l x + m y - z = 9,

then

l^{2} + m^{2}

is equal to