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

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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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Important Questions on Three Dimensional Geometry

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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

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 50

The shortest distance between the lines

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

and

\frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4},

lies in the interval:

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 51

The lines

6 x = 3 y = 2 z

and

\frac{x - 1}{- 2} = \frac{y - 2}{- 4} = \frac{z - 3}{- 6}

are

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 52

The lines

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

and

\frac{x - 1}{- 2} = \frac{y - 2}{- 4} = \frac{z - 3}{- 6}

are

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Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 53

Equation of the line of the shortest distance between the lines

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

and

\frac{x - 1}{0} = \frac{y + 1}{- 2} = \frac{z}{1}

is