Question and Answers Forum

All Questions      Topic List

Coordinate Geometry Questions

Previous in All Question      Next in All Question      

Previous in Coordinate Geometry      Next in Coordinate Geometry      

Question Number 95779 by i jagooll last updated on 27/May/20

$$\mathrm{if}\mathrm{plane}3\mathrm{x}+4\mathrm{y}+\mathrm{tz}=2\mathrm{and}$$$$\mathrm{kx}+6\mathrm{y}+5\mathrm{z}-2=0\mathrm{are}\mathrm{parallel}.$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{k}\mathrm{and}\mathrm{t}$$

Answered by john santu last updated on 27/May/20

$$\frac{3}{\mathrm{k}}=\frac{4}{6}=\frac{\mathrm{t}}{5}$$$$\{\begin{array}{l}\mathrm{k}=\frac{18}{4}=\frac{9}{2}\\ \mathrm{t}=\frac{20}{6}=\frac{10}{3}\end{array}$$$$$$

Commented by i jagooll last updated on 27/May/20

$$\mathrm{thank}\mathrm{you}$$

Answered by Rio Michael last updated on 28/May/20

$$\mathrm{normal}\mathrm{for}\mathrm{plane}1n_1=3i+4j+tk$$$$\mathrm{normal}\mathrm{for}\mathrm{plane}2n_2=ki+6j+5k$$$$\mathrm{for}\mathrm{parrallel}\mathrm{vectors}\overrightarrow{a}\mathrm{and}\overrightarrow{b},\overrightarrow{a}=h\overrightarrow{b}\mathrm{where}h\mathrm{is}\mathrm{a}\mathrm{constant}h\in \mathbb{R}$$$$\Rightarrow (3i+4j+tk)=h(ki+6j+5k)$$$$\Rightarrow 4=6h\iff h=\frac{2}{3}$$$$\mathrm{also}3=hk\Rightarrow k=\frac{3}{h}=3\times \frac{3}{2},k=\frac{9}{2}$$$$\mathrm{and}t=5h\Rightarrow t=\frac{10}{3}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com