24-Three Dimensional Geometry

Three Dimensional Geometry

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stax1212
ABCD is a regular tetrahedron with side length ($\sqrt{2}$ + 1) units. A point P is taken on the edge AB ...?
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Abhineet
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stax1212
Let A and B are points on the line L_{1} L_{2} respectively such that d = OA + OB + AB is minimum (O being the origin), match the following ... ?
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Abhineet
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M
How to prepare for Three Dimensional Geometry for JEE Mains
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Moderator2
M
A
Direction cosines of a line joining A(5,-3,8) and B(7,-5,9) are?
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rahulp
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If $\mathrm{A}(3,2,3), \mathrm{B}(1,4,6)$ and $\mathrm{C}(7,4,5)$ are the three vertices of a parallelogram ABCD , then the angle between its
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246
solution.livedoubt
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K
If $A(3,2,3), B(1,4,6)$ and $C(7,4,5)$ are the three vertices of a parallelogram $A B C D$, then the angle betweer its diagonal through D and the side
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1
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292
solution.livedoubt
S
Aspirant
Let $A(6,8), B(10 \cos \alpha,-10 \sin \alpha)$ and $C(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle. If $L(a, 9)$ and $G(h, k)$ be
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374
solution.livedoubt
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AGRIMA M
Let the lines \( \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2} \) and \( \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z-28}{\lambda} \) be coplanar and ...
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Math.LiveDoubtClearing
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A
Let \( \mathrm{A}(2 \hat{i}+3 \hat{j}+5 \hat{k}), B(-\hat{i}+3 \hat{j}+2 \hat{k}) \) and \( C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k}) \) are vertices
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201
Math.LiveDoubtClearing
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R
Find the angle between the lines whose direction cosines are given by $l+m+n=0$ and $2l^2+ 2m^2- n^2=0.$
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3
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286
Math.LiveDoubtClearing
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S
Let the co-ordinates of one vertex of \( \triangle A B C \) be \( A(0,2, \alpha) \) and the other two vertices lie on the line
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1
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287
Math.LiveDoubtClearing
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M
Find the length of perpendicular from P(5,8,1) to line\[\frac{x+1}{2}=\frac{y-3}{5}=\frac{z-8}{1}\]
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1
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183
LiveDoubtClearing
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deveshgarg2008
The length of two opposite edges of a tetrahedron are 12 and 15 units and the shortest distance between them is 10 units. If the volume of the ...
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1
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367
Math.LiveDoubtClearing
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P
The distance of the point $Q(0,2,-2)$ form the line passing through the point $P(5,-4,3)$ and perpendicular to the lines
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1
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250
LiveDoubtClearing
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P
If the shortest distance between the lines $\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$ and $\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}$ is ...
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1
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239
Math.LiveDoubtClearing
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P
Let the line L intersect the lines \[ x-2=-y=z-1,2(x+1)=2(y-1)=z \] and be parallel to the line \( \frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2} \).
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1
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2K
Math.LiveDoubtClearing
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sumit_wadhwa1
Find the shortest distance between the lines $\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1} \text { and } \frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$.
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1
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196
Math.LiveDoubtClearing
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sumit_wadhwa1
Show that the lines $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\frac{x-2}{1}=\frac{y-4}{3}=\frac{z-6}{5}$ intersect. Also find their point of
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1
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204
Math.LiveDoubtClearing
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sumit_wadhwa1
Find the foot of the perpendicular from the point \( (2,3,-8) \) to the line \( \frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3} \).
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1
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204
Math.LiveDoubtClearing
M
A
If the shortest distance between the lines $\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$ and $\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}$ is ...
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1
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865
LiveDoubtClearing
L
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