Question Number 45575 by rahul 19 last updated on 14/Oct/18 Commented by rahul 19 last updated on 14/Oct/18 $${My}\:{doubt}: \\ $$$${If}\:{i}\:{will}\:{take}\:{both}\:{points}\:{on}\:{same}\:{side} \\ $$$${of}\:{plane}\:\left({wrong}\:{method}\right)\:{and}\:{will} \\ $$$${take}\:{points}\:{on}\:{opposite}\:{side}\:{i}\:{will}\:{get}\:…
Question Number 45555 by rahul 19 last updated on 14/Oct/18 $${Prove}\:{that}\:{points}\:\left(\mathrm{4},−\mathrm{1},\mathrm{3}\right)\:\&\:\left(\mathrm{5},−\mathrm{1},\mathrm{4}\right) \\ $$$${lies}\:{on}\:{same}\:{side}\:{of}\:{the}\:{plane}\:{x}+{y}+{z}=\mathrm{7}. \\ $$ Commented by rahul 19 last updated on 14/Oct/18 Answered by…
Question Number 111006 by pete last updated on 01/Sep/20 $$\mathrm{The}\:\mathrm{vectors}\:\boldsymbol{\mathrm{p}},\boldsymbol{\mathrm{q}}\:\mathrm{and}\:\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{mutially}\:\mathrm{perpendicularwith} \\ $$$$\mid\boldsymbol{\mathrm{q}}\mid=\mathrm{3}\:\mathrm{and}\:\mid\boldsymbol{\mathrm{r}}\mid=\sqrt{\mathrm{5}.\mathrm{4}\:}\:.\mathrm{If}\:\mathrm{X}=\:\mathrm{7}\boldsymbol{\mathrm{p}}+\mathrm{5}\boldsymbol{\mathrm{q}}+\mathrm{7}\boldsymbol{\mathrm{r}}\:\mathrm{and} \\ $$$$\mathrm{Y}=\mathrm{2}\boldsymbol{\mathrm{p}}+\mathrm{3}\boldsymbol{\mathrm{q}}−\mathrm{5}\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{perpendicular},\:\mathrm{find}\mid\boldsymbol{\mathrm{p}}\mid. \\ $$ Commented by kaivan.ahmadi last updated on 01/Sep/20 $${p}.{q}={p}.{r}={q}.{r}=\mathrm{0} \\…
Question Number 45417 by rahul 19 last updated on 12/Oct/18 $${Find}\:{image}\:{of}\:{plane}\:{x}−{y}+{z}−\mathrm{3}=\mathrm{0}\:{in}\: \\ $$$${plane}\:\mathrm{2}{x}+{y}−{z}+\mathrm{4}=\mathrm{0}\:? \\ $$ Answered by MrW3 last updated on 13/Oct/18 $${since}\:{both}\:{planes}\:{are}\:{perpendicular} \\ $$$${to}\:{each}\:{other},\:{the}\:{image}\:{is}\:{itself},\:{i}.{e}.…
Question Number 45259 by rahul 19 last updated on 11/Oct/18 $${Find}\:\:{distance}\:{of}\:{point}\:\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:{from} \\ $$$${the}\:{line}\:{passing}\:{through}\:\left(\mathrm{2},\mathrm{3},\mathrm{4}\right)\:\& \\ $$$$\left(−\mathrm{1},\mathrm{2},\mathrm{3}\right)\:? \\ $$ Commented by rahul 19 last updated on 11/Oct/18…
Question Number 44848 by pieroo last updated on 05/Oct/18 $$\left(\mathrm{1}\right)\:\mathrm{If}\:\overset{\rightarrow} {\boldsymbol{\mathrm{a}}}=\mathrm{a}_{\mathrm{1i}} +\mathrm{a}_{\mathrm{2j}} +\mathrm{a}_{\mathrm{3k}} \:\mathrm{and}\:\overset{\rightarrow} {\boldsymbol{\mathrm{b}}}=\mathrm{b}_{\mathrm{1i}} +\mathrm{b}_{\mathrm{2j}} +\mathrm{b}_{\mathrm{3k}} \:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{i}.\:\overset{\rightarrow} {\boldsymbol{\mathrm{a}}}×\overset{\rightarrow} {\boldsymbol{\mathrm{b}}}=\begin{vmatrix}{\mathrm{i}}&{\mathrm{j}}&{\mathrm{k}}\\{\mathrm{a}_{\mathrm{1}} }&{\mathrm{a}_{\mathrm{2}} }&{\mathrm{a}_{\mathrm{3}} }\\{\mathrm{b}_{\mathrm{1}}…
Question Number 44035 by rahul 19 last updated on 20/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on 20/Sep/18 $$\left(\overset{\rightarrow} {{x}}.\overset{\rightarrow} {{z}}\right)\overset{\rightarrow} {{y}}−\left(\overset{\rightarrow} {{x}}.\overset{\rightarrow} {{y}}\right)\overset{\rightarrow} {{z}}=\overset{\rightarrow} {{a}}…
Question Number 44020 by rahul 19 last updated on 20/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 20/Sep/18 $$\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{d}}=\mid\overset{\rightarrow} {{a}}\mid{cos}\theta_{\mathrm{1}} \:\:\:\:\overset{\rightarrow} {{b}}.\overset{\rightarrow} {{d}}=\mid\overset{\rightarrow} {{b}}\mid{cos}\theta_{\mathrm{2}}…
Question Number 43856 by MASANJA J last updated on 16/Sep/18 $${given}\:{that} \\ $$$${a}×{b}=\mathrm{3}{i}\:+\:{j}\:+{k} \\ $$$${a}×{c}=−{i}\:−\mathrm{2}{j}\:+{k} \\ $$$${find} \\ $$$$\left.{i}\right){c}×{a} \\ $$$$\left.{ii}\right){a}×\left({b}×{c}\right) \\ $$$$\left.{iii}\right)\left({a}×{b}\right)\bullet\left({a}×{c}\right) \\ $$…
Question Number 174489 by pete last updated on 02/Aug/22 $$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{have}\:\mathrm{position}\:\mathrm{vectors} \\ $$$$\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{respectively}\:\mathrm{reffrred}\:\mathrm{to}\:\mathrm{an}\:\mathrm{origin}\:\mathrm{O}. \\ $$$$\mathrm{i}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{X}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{AB}\:\mathrm{produced} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{AB}\::\:\mathrm{BX}=\mathrm{2}:\mathrm{1},\:\mathrm{find}\:{x},\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{vector}\:\mathrm{of}\:\mathrm{X}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}. \\ $$$$\mathrm{ii}.\:\mathrm{if}\:\mathrm{Y}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{BC},\:\mathrm{between}\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{BY}\::\:\mathrm{YC}\:=\:\mathrm{1}:\mathrm{3},\:\mathrm{find}\:{y},\:\mathrm{the}\:\mathrm{position}\:\mathrm{vector} \\ $$$$\mathrm{of}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}. \\…