The three planes $x+y=0,y+z=0$ and $x+z=0$

Important Questions on Three Dimensional Geometry

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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 30

The equation of the sphere concentric with the sphere $x^2+y^2+z^2-2x-4y+6z+10=0$ and of double its surface area is $x^2+y^2+z^2-2x-4y+6z+k=0$, then $k=$

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 31

The shortest distance between the lines $\frac{x-7}{3}=\frac{y+4}{-16}=\frac{z-6}{7}$ and $\frac{x-10}{3}=\frac{y-30}{8}=\frac{4-z}{5}$ 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 33

The shortest distance between the lines $x=y+2=6z-6$ and $x+1=2y=-12z$ 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 2>Q 1

A line segment has length $63$ and direction ratios are $3,-2,6$. If the line makes an obtuse angle with $x$-axis, the components of the line vector are 

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 2>Q 2

The centre of sphere passes through four points $\left(0,0,0\right),\left(0,2,0\right),\left(1,0,0\right)$ and $\left(0,0,4\right)$ 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 2>Q 3

The coordinates of the point where the line through the points $A\left(3,4,1\right)$ and $B\left(5,1,6\right)$ crosses the $XY$-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 2>Q 4

A plane passes through a fixed point $\left(a,b,c\right)$. The locus of the foot of perpendicular to it from the origin is a sphere of radius

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 2>Q 5

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, if