Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 41

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The shortest distance between the lines $\frac{x - 2}{3} = \frac{y + 3}{4} = \frac{z - 1}{5}$ and $\frac{x - 5}{1} = \frac{y - 1}{2} = \frac{z - 6}{3} i s$

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Important Questions on Three Dimensional Geometry

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 42

The length of the shortest distance between the two lines

\vec{r} = (- 3 \hat{i} + 6 \hat{j}) + s (- 4 \hat{i} + 3 \hat{j} + 2 \hat{k})

and

\vec{r} = (- 2 \hat{i} + 7 \hat{k}) + t (- 4 \hat{i} + \hat{j} + \hat{k})

is:

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 43

The shortest distance between the lines

\vec{r} = \vec{a} + k \vec{b}

and

\vec{r} = \vec{a} + l \vec{c}

is (where

\vec{b}

and

\vec{c}

are non-collinear)

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 44

The shortest distance between lines

\frac{x - 3}{2} = \frac{y + 15}{- 7} = \frac{z - 9}{5}

and

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

is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 45

The length of the shortest distance between the two lines

\vec{r} = (- 3 \hat{\dot{i}} + 6 \hat{\dot{j}}) + s (- 4 \hat{\dot{i}} + 3 \hat{\dot{j}} + 2 \hat{k})

and

\vec{r} = (- 2 \hat{\dot{i}} + 7 \hat{k}) + t (- 4 \hat{\dot{i}} + \hat{\dot{j}} + \hat{k})

is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 46

The lines

\vec{r} = i - j + λ (2 i + k)

and

\vec{r} = (2 i - j) + μ (i + j - k)

intersect for

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 47

A point moves in such a way that the sum of its distance from

x y

-plane and

y z

-plane remains equal to its distance from

z x

-plane. The locus of the point is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 48

A square

A B C D

of diagonal

2 a

is folded along the diagonal

A C

so that the planes

D A C

and

B A C

are at right angle. The shortest distance between

D C

and

A B

is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 49

The edge of a cube is of length

' a'

then the shortest distance between the diagonal of a cube and an edge skew to it is