Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 28

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IMPORTANT

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The perpendicular distance of the point $(2, 4, - 1)$ from the line $\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{- 9}$ is

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Important Questions on Three Dimensional Geometry

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 29

The foot of the perpendicular from

(0, 2, 3)

to the line

\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 30

Let

λ

be an integer. If the shortest distance between the lines

x - λ = 2 y - 1 = - 2 z

and

x = y + 2 λ = z - λ

is

\frac{\sqrt{7}}{2 \sqrt{2}},

then the value of

|λ|

is _______.

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 31

If the lines

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

and

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

are coplanar, then

\sin^{- 1} (\sin λ) + \cos^{- 1} (\cos λ) =

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 32

The vector equation of line passing through

(2, - 1, 1)

and parallel to the line

\vec{r} = 3 \hat{i} - \hat{j} + 2 \hat{k} + λ (2 \hat{i} + 7 \hat{j} - 3 \hat{k})

is

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 33

The two lines

L_{1} : \vec{r} = (\hat{i} + 5 \hat{j} + 5 \hat{k}) + t (4 \hat{i} - 4 \hat{j} + 5 \hat{k})

and

L_{2} : \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + s (8 \hat{i} - 3 \hat{j} + \hat{k})

are such that

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Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 34

If the lines

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

and

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

are co-planar, then the value of

k

is _______.

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 35

The length of perpendicular from

(1, 6, 3)

to the line

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

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 28 - Three Dimensional Geometry>Level 1>Q 36

If

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

is the equation of the line through

(1, 2, - 1)

and

(- 1, 0, 1)

, then

(l, m, n)

is