Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 119160 by zakirullah last updated on 22/Oct/20

Commented by zakirullah last updated on 22/Oct/20

find the position vecter of a point R  which divides the line joining  the point whose the position  vecters are P(i+2j−k),Q(−i+j+k) in  the ratio 2:1 internaly and externaly

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{position}}\:\boldsymbol{\mathrm{vecter}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{{p}\mathrm{oint}}\:\boldsymbol{\mathrm{R}} \\ $$$$\boldsymbol{{which}}\:\boldsymbol{{divides}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\boldsymbol{{joining}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{point}}\:\boldsymbol{{whose}}\:\boldsymbol{{the}}\:\boldsymbol{{position}} \\ $$$$\boldsymbol{{vecters}}\:\boldsymbol{{are}}\:\boldsymbol{{P}}\left(\boldsymbol{{i}}+\mathrm{2}\boldsymbol{{j}}−\boldsymbol{{k}}\right),\boldsymbol{{Q}}\left(−\boldsymbol{{i}}+\boldsymbol{{j}}+\boldsymbol{{k}}\right)\:\boldsymbol{{in}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{ratio}}\:\mathrm{2}:\mathrm{1}\:\boldsymbol{{internaly}}\:\boldsymbol{{and}}\:\boldsymbol{{externaly}} \\ $$

Commented by zakirullah last updated on 22/Oct/20

Please help??⇈

$$\boldsymbol{{Please}}\:\boldsymbol{{help}}??\upuparrows \\ $$

Commented by PRITHWISH SEN 2 last updated on 22/Oct/20

R = (((2×(−1)+1)/3) ,((2×1+1×2)/3) ,((2×1+1×(−1))/3))  R    = (−(1/3),(4/3),(1/3))  the position vector   = −(1/3)i^� +(4/3)j^� +(1/3)k^�   (for internally )

$$\mathrm{R}\:=\:\left(\frac{\mathrm{2}×\left(−\mathrm{1}\right)+\mathrm{1}}{\mathrm{3}}\:,\frac{\mathrm{2}×\mathrm{1}+\mathrm{1}×\mathrm{2}}{\mathrm{3}}\:,\frac{\mathrm{2}×\mathrm{1}+\mathrm{1}×\left(−\mathrm{1}\right)}{\mathrm{3}}\right) \\ $$$$\mathrm{R}\:\:\:\:=\:\left(−\frac{\mathrm{1}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{3}},\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\mathrm{the}\:\mathrm{position}\:\mathrm{vector} \\ $$$$\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\hat {\boldsymbol{\mathrm{i}}}+\frac{\mathrm{4}}{\mathrm{3}}\hat {\boldsymbol{\mathrm{j}}}+\frac{\mathrm{1}}{\mathrm{3}}\hat {\boldsymbol{\mathrm{k}}}\:\:\left(\mathrm{for}\:\mathrm{internally}\:\right) \\ $$

Commented by zakirullah last updated on 22/Oct/20

sorry sir i think this mathod is  very high  please can you explain it in another way?

$$\boldsymbol{{sorry}}\:\boldsymbol{{sir}}\:\boldsymbol{{i}}\:\boldsymbol{{think}}\:\boldsymbol{{this}}\:\boldsymbol{{mathod}}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{very}}\:\boldsymbol{{high}} \\ $$$$\boldsymbol{{please}}\:\boldsymbol{{can}}\:\boldsymbol{{you}}\:\boldsymbol{{explain}}\:\boldsymbol{{it}}\:\boldsymbol{{in}}\:\boldsymbol{{another}}\:\boldsymbol{{way}}? \\ $$

Commented by PRITHWISH SEN 2 last updated on 22/Oct/20

think P and Q as points in 3D  then P=(1,2,−1) & Q=(−1,1,1)  and find R as internally divides PQ in the   ratio 2:1 by the use of section fomula.  then just put it with i,j,k.

$$\mathrm{think}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}\:\mathrm{as}\:\mathrm{points}\:\mathrm{in}\:\mathrm{3D} \\ $$$$\mathrm{then}\:\mathrm{P}=\left(\mathrm{1},\mathrm{2},−\mathrm{1}\right)\:\&\:\mathrm{Q}=\left(−\mathrm{1},\mathrm{1},\mathrm{1}\right) \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{R}\:\mathrm{as}\:\mathrm{internally}\:\mathrm{divides}\:\mathrm{PQ}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{ratio}\:\mathrm{2}:\mathrm{1}\:\mathrm{by}\:\mathrm{the}\:\mathrm{use}\:\mathrm{of}\:\mathrm{section}\:\mathrm{fomula}. \\ $$$$\mathrm{then}\:\mathrm{just}\:\mathrm{put}\:\mathrm{it}\:\mathrm{with}\:\boldsymbol{\mathrm{i}},\boldsymbol{\mathrm{j}},\boldsymbol{\mathrm{k}}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com