EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Three Dimensional Geometry>GUJCET 2018>Q 3

MEDIUM

GUJCET

IMPORTANT

Earn 100

Lines $\vec{r} = (3 + t) \hat{i} + (1 - t) \hat{j} + (- 2 - 2 t) \hat{k}, t \in R$ and $x = 4 + k, y = - k, z = - 4 - 2 k, k \in R,$ then relation between lines is

50% studentsanswered this correctly

Important Questions on Three Dimensional Geometry

MEDIUM

GUJCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Three Dimensional Geometry>GUJCET 2017>Q 4

Plane

a x + b y + c z = 1

intersect axes in

A, B, C

respectively. If

G (\frac{1}{6}, - \frac{1}{3}, 1)

is the centroid of

Δ A B C,

then

a + b + 3 c =

_______.

MEDIUM

GUJCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Three Dimensional Geometry>GUJCET 2017>Q 5

If the normal of the plane makes an angles

\frac{π}{4}, \frac{π}{4}

and

\frac{π}{2}

with positive

X

-axis,

Y

-axis and

Z

-axis respectively and the length of the perpendicular line segment from origin to the plane is

\sqrt{2},

then the equation of the plane is ______.

EASY

GUJCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Three Dimensional Geometry>GUJCET 2018>Q 6

If a plane has

X

-intercept

l, Y

-intercept

m

and

Z -

intercept

n,

and perpendicular distance of plane from origin is

k,

then

HARD

GUJCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Three Dimensional Geometry>GUJCET 2018>Q 7

The equation of plane containing intersecting lines

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

and

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

is