Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 15

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The non zero value of $a$ for which the line $2 x - y + 3 z + 4 = 0 = a x + y - z + 2$ and $x - 3 y + z = 0 = x + 2 y + z + 1$ are co-planar is

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Important Questions on Three Dimensional Geometry

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 16

If the equation of plane passing through the mirror image of a point

(2, 3, 1)

with respect to line

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

and containing the line

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

is

α x + β y + γ z = 24

then

α + β + γ

is equal to:

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 17

Let

L

be the line of intersection of planes

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

and

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

If

P (α, β, γ)

is the foot of perpendicular on

L

from the point

(1, 2, 0),

then the value of

35 (α + β + γ)

is equal to:

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 18

Three distinct lines

\frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 3}{1}, \frac{x - 1}{5} = \frac{2 y - 4}{3} = \frac{3 z - 9}{1}, \frac{x - λ^{2}}{3} = \frac{y - 2}{2} = \frac{z - 3}{λ}

are concurrent the value of

λ

may be

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 19

The equation of the plane passing through

Z

-axis and perpendicular to line

\frac{x - 1}{\cos θ} = \frac{y + 2}{\sin θ} = \frac{z - 3}{0}

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 20

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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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 21

The equation of the set of point

P

, the sum of whose distances from

A (4, 0, 0)

and

B (- 4, 0, 0)

is equal to

10

, is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 22

Consider the line

L

given by the equation

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

Let

Q

be the mirror image of the point

(2, 3, - 1)

with respect to

L .

Let a plane

P

be such that it passes through

Q,

and the line

L

is perpendicular to

P .

Then which of the following points is on the plane

P ?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 3>Q 23

The reflection of the point

\vec{a}

in the plane

\vec{r} \cdot \vec{n} = q

is