The lines whose vector equations areratbrctd 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

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 17

The volume of the tetrahedron included between the plane

3 x + 4 y - 5 z - 60 = 0

and the coordinate planes 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 18

Distance between two parallel planes

2 x + y + 2 z = 8

and

4 x + 2 y + 4 z + 5 = 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 19

Given the line

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

and the plane

π : x - 2 y - z = 0

. From the following assertions, the only statement that is always true 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 20

Let

A (\vec{a})

and

B (\vec{b})

be points on the two skew lines

\vec{r} = \vec{a} + λ \vec{p}

and

\vec{r} = \vec{b} + μ \vec{q}

and the shortest distance between the skew lines is

1

, where

\vec{p}

and

\vec{q}

are unit vectors forming adjacent sides of a parallelogram enclosing an area of

\frac{1}{2} units

. If an angle between

A B

and the line of the shortest distance is

60 °

, then

A B =

MEDIUM

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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 21

If plane

2 x + 3 y + 6 z + k = 0

is tangent to the sphere

x^{2} + y^{2} + z^{2} + 2 x - 2 y + 2 z - 6 = 0

, then the value of

k

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 22

A variable plane moves so that the sum of reciprocals of its intercepts on the three coordinate axes is constant

λ

. It passes through a fixed point, which has coordinates

The lines whose vector equations are $\vec{r} = \vec{a} + t \vec{b}, \vec{r} = \vec{c} + t^{'} \vec{d}$ are coplanar if

Important Questions on Three Dimensional Geometry

Learn and Prepare for any exam you want !

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

Important Questions on Three Dimensional Geometry

Learn and Prepare for any exam you want !

The lines whose vector equations are $\vec{r} = \vec{a} + t \vec{b}, \vec{r} = \vec{c} + t^{'} \vec{d}$ are coplanar if