Class 12MathematicsTHREE DIMENSIONAL GEOMETRYSystem of co-ordinates, Direction cosines and direction ratios, Projection
EasyIf $\ell, m, n$ and $a, b, c$ are direction cosines of two lines, then:
- Athey are parallel when $\ell a + mb + nc = 0$
- Bthey are perpendicular when $\frac{\ell}{a} = \frac{m}{b} = \frac{n}{c}$
- Cthe direction ratios of the bisectors of the angles between the two lines are $\ell \pm a, m \pm b, n \pm c$
- Dthe direction ratios of the bisectors of the angles between the two lines are $\ell a, mb, nc$
Explore More
Similar Questions
The angle between the lines with direction ratios $\left( \frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2} \right)$ and $\left( \frac{\sqrt{3}}{4}, \frac{1}{4}, -\frac{\sqrt{3}}{2} \right)$ is ......... $^o$.
Easy
View SolutionIf $< a, b, c >$ and $< a', b', c' >$ are the direction ratios of two perpendicular lines,then which of the following is true?
Easy
View SolutionIf $O \equiv (0, 0, 0)$ and $P \equiv (1, \sqrt{2}, 1)$,then the acute angles made by the line $OP$ with $XOY$,$YOZ$,and $ZOX$ planes are,respectively:
If the lengths of projections of a line of length $l$ over the coordinate axes are $l_1, l_2$ and $l_3$ respectively,then $l_1^2+l_2^2+l_3^2$ is equal to
If the projections of a line segment on the coordinate axes are $3, 4,$ and $5$,then its length is:
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo