The lines whose vector equations are r → = a → + t b → , r → = c → + t ' d → are coplanar if

a → - c → · b → × d → = 0

a → + b → · c → × d → = 0

b → - c → · a → × d → = 0

b → - d → · a → × c → = 0

If a plane meets the coordinate axes in ABC such that the centroid of the triangle is the point1rr2then equation of the plane is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 9

The shortest distance from the plane

12 x + 4 y + 3 z = 327

to the sphere

x^{2} + y^{2} + z^{2} + 4 x - 2 y - 6 z = 155

is

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 10

The equation of the plane containing the line

\frac{x - x_{1}}{l} = \frac{y - y_{1}}{m} = \frac{z - z_{1}}{n}

is

a (x - x_{1}) + b (y - y_{1}) + c (z - z_{1}) = 0

.

Correct option is

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 11

A line makes the same angle

θ

, with each of the

x

and

z

-axis. If the angle

β

, which it makes with

y

-axis, is such that

\sin^{2} β = 3 \sin^{2} θ

, then

\cos^{2} θ

equal

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 12

If the foot of the perpendicular from the origin to a plane is

P (a, b, c)

the equation of the plane is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 13

If the points

(1, 2, 3)

and

(2, - 1, 0)

lie on the opposite sides of the plane

2 x + 3 y - 2 z = k

, then

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 14

The lines whose vector equations are

\vec{r} = \vec{a} + t \vec{b}, \vec{r} = \vec{c} + t^{'} \vec{d}

are coplanar if

EASY

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 15

Equation of a plane bisecting the angles between the planes

2 x - y + 2 z + 3 = 0

and

3 x - 2 y + 6 z + 8 = 0

is

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 16 - Three Dimensional Geometry>Exercise 1>Q 16

Equation of plane which passes through the point of intersection of lines

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

and

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

and at greatest distance from the point

(0, 0, 0)

is

If a plane meets the co-ordinate axes in $A, B, C$ such that the centroid of the triangle is the point $(1, r, r^{2})$ , then equation of the plane is

Important Questions on Three Dimensional Geometry

Learn and Prepare for any exam you want !

If a plane meets the co-ordinate axes in A,B,C such that the centroid of the triangle is the point 1,r,r2, then equation of the plane is

Important Questions on Three Dimensional Geometry

Learn and Prepare for any exam you want !

If a plane meets the co-ordinate axes in $A, B, C$ such that the centroid of the triangle is the point $(1, r, r^{2})$ , then equation of the plane is