Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 10

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IMPORTANT

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The angle between two diagonals of a cube will be

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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 2>Q 11

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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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 12

Vector equation of the plane

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

in the scalar dot product form is

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 13

The equation of a plane passing through the line of intersection of the planes

x + 2 y + 3 z = 2

and

x - y + z = 3

and at a distance

\frac{2}{\sqrt{3}}

from the point

(3, 1, - 1)

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 14

The equation of plane passing through

(2, 1, 0)

and line of intersection of planes

x - 2 y + 3 z = 4

and

x - y + z = 3

is

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 15

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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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 16

A tetrahedron has vertices

O (0, 0, 0), A (1, 2, 1),

B (2, 1, 3)

and

C (- 1, 1, 2) .

Then the angle between the planes

O A B

and

A B C

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 17

The lines

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

and

\frac{x - 3}{1} = \frac{y - 6}{2} = \frac{z}{1}

intersect each other at point

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 2>Q 18

The direction ratios of the line

x - y + z - 5 = 0 = x - 3 y - 6

are