Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 7

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A plane passes through the points $P (4, 0, 0)$ and $Q (0, 0, 4)$ and is parallel to the $Y$ -axis. The distance of the plane from the origin is

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Important Questions on Three Dimensional Geometry

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 8

The distance between the parallel planes given by the equations

\vec{r} \cdot (2 \hat{i} - 2 \hat{j} + \hat{k}) + 3 = 0

and

\vec{r} \cdot (4 \hat{i} - 4 \hat{j} + 2 \hat{k}) + 5 = 0

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 9

A variable plane forms a tetrahedron of constant volume

64 k^{3}

with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 10

The equation of the plane containing the line

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

and the point

(0, 7, - 7)

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 11

Which one of the following lines is parallel to the line

$L : (x, y, z) = (1, 0, - 2) + t (- 1, 3, 0), t \in R$

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 12

Consider the plane

(x, y, z) = (0, 1, 1) + λ (1, - 1, 1) + μ (2, - 1, 0)

. The distance of this plane from the origin is

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 13

The value of

m

, for which straight line

3 x - 2 y + z + 3 = 0 = 4 x - 3 y + 4 z + 1

is parallel to the plane

2 x - y + m z - 2 = 0

, is

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 14

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, if

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Beta Question Bank for Engineering: Mathematics>Chapter 22 - Three Dimensional Geometry>EXERCISE-1>Q 15

The value of

a

for which the lines

\frac{x - 2}{1} = \frac{y - 9}{2} = \frac{z - 13}{3}

and

\frac{x - a}{- 1} = \frac{y - 7}{2} = \frac{z + 2}{- 3}

intersect, is