HARD

JEE Main

IMPORTANT

Earn 100

A perpendicular is drawn from a point on the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z}{1}$ to the plane $x + y + z = 3$ such that the foot of the perpendicular $Q$ also lies on the plane $x - y + z = 3$ . Then the coordinates of $Q$ are

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Important Questions on Three Dimensional Geometry

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 10th January 2019 Shift 1>Q 89

The plane passing through the point

(4, - 1, 2)

and parallel to the lines

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

and

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

also passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 10th January 2019 Shift 1>Q 90

Let

A

be a point on the line

\vec{r} = (1 - 3 μ) \hat{i} + (μ - 1) \hat{j} + (2 + 5 μ) \hat{k}

and

B (3, 2, 6)

be a point in the space. Then the value of

μ

for which the vector

\vec{A B}

is parallel to the plane

x - 4 y + 3 z = 1

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 10th January 2019 Shift 2>Q 91

The plane which bisects the line segment joining the points

(- 3, - 3, 4)

and

(3, 7, 6)

at right angles, passes through which one of the following points?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 10th January 2019 Shift 2>Q 92

On which of the following lines lies the point of intersection of the line,

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

and the plane,

x + y + z = 2 ?

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 12th April 2019 Shift 1>Q 93

If the line

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

intersects the plane

2 x + 3 y - z + 13 = 0

at a point

P

and the plane

3 x + y + 4 z = 16

at a point

Q,

then

P Q

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 12th April 2019 Shift 2>Q 94

A plane which bisects the angle between the two given planes

2 x - y + 2 z - 4 = 0

and

x + 2 y + 2 z - 2 = 0

, passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 12th April 2019 Shift 2>Q 95

The length of the perpendicular drawn from the point

(2, 1, 4)

to the plane containing the lines

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

and

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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 12th January 2019 Shift 1>Q 96

A tetrahedron has vertices

P (1, 2, 1), Q (2, 1, 3), R (- 1, 1, 2)

and

O (0, 0, 0)

. The angle between the faces

O P Q

and

P Q R

A perpendicular is drawn from a point on the line x-12= y+1-1=z1 to the plane x+y+z=3 such that the foot of the perpendicular Q also lies on the plane x-y+z=3. Then the coordinates of Q are

Important Questions on Three Dimensional Geometry

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A perpendicular is drawn from a point on the line $\frac{x - 1}{2} = \frac{y + 1}{- 1} = \frac{z}{1}$ to the plane $x + y + z = 3$ such that the foot of the perpendicular $Q$ also lies on the plane $x - y + z = 3$ . Then the coordinates of $Q$ are