Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 79

EASY

CUET (UG)

IMPORTANT

Earn 100

If the lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}$ and $\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar, then $k$ can have

40% studentsanswered this correctly

Important Questions on Three Dimensional Geometry

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 80

The point of intersection of the lines

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

and

\frac{x - 4}{5} = \frac{y - 1}{2} = z i s

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 81

The number of distinct real values of

λ

, for which the lines

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

and

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

, are coplanar is

HARD

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 82

The lines

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

and

y - x = 0 = x - z + λ

are coplanar for:

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 83

The equation of the plane parallel to the plane

x + y + z = 0

and passing through

(α, β, γ)

is

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 84

The equation

x^{2} - x - 2 = 0

in three dimensional space is represented by

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 85

The angle between the planes

2 x - y + z = 6

and

x + y + 2 z = 7

is:

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 86

The planes

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - 6 \hat{k}) = 7

and

\vec{r} \cdot (\frac{- 2}{7} \hat{i} - \frac{3}{7} \hat{j} + \frac{6}{7} \hat{k}) = 0

are:

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 11 - Three Dimensional Geometry>Exercise>Q 87

The acute angle between the planes

2 x - y + z = 6

and

x + y + 2 z = 3

is