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

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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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Important Questions on Three Dimensional Geometry

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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

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 38

The distance (in units) of the point

(1, - 5, 9)

from plane

x - y + z = 5

measured along the line

x = y = z

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 39

If the image of the point

P (1, - 2, 3)

in the plane,

2 x + 3 y - 4 z + 22 = 0

measured parallel to the line,

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

is

Q

, then

P Q

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 40

The distance of the point

(1, 3, - 7)

from the plane passing through the point

(1, - 1, - 1)

, having normal perpendicular to both the lines

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

and

\frac{x - 2}{2} = \frac{y + 1}{- 1} = \frac{z + 7}{- 1}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 41

The length of the projection of the line segment joining the points

(5, - 1, 4)

and

(4, - 1, 3)

on the plane,

x + y + z = 7

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 21 - Three Dimensional Geometry>Exercise-3>Q 42

If the lines

x = a y + b, z = c y + d

and

x = a^{'} z + b^{'}, y = c^{'} z + d^{'}

are perpendicular, then :