Category: Vector

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 174489 by pete last updated on 02/Aug/22 $$\mathrm{The}\mathrm{points}\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{have}\mathrm{position}\mathrm{vectors}$$$$\mathbf{a},\mathbf{b}\mathrm{and}\mathbf{c}\mathrm{respectively}\mathrm{reffrred}\mathrm{to}\mathrm{an}\mathrm{origin}\mathrm{O}.$$$$\mathrm{i}.\mathrm{Given}\mathrm{that}\mathrm{the}\mathrm{point}\mathrm{X}\mathrm{lie}\mathrm{on}\mathrm{AB}\mathrm{produced}$$$$\mathrm{so}\mathrm{that}\mathrm{AB}:\mathrm{BX}=2:1,\mathrm{find}x,\mathrm{the}\mathrm{position}$$$$\mathrm{vector}\mathrm{of}\mathrm{X}\mathrm{in}\mathrm{terms}\mathrm{of}\mathbf{b}\mathrm{and}\mathbf{c}.$$$$\mathrm{ii}.\mathrm{if}\mathrm{Y}\mathrm{lies}\mathrm{on}\mathrm{BC},\mathrm{between}\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{so}\mathrm{that}$$$$\mathrm{BY}:\mathrm{YC}=1:3,\mathrm{find}y,\mathrm{the}\mathrm{position}\mathrm{vector}$$$$\mathrm{of}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}. \…

Question Number 42711 by rahul 19 last updated on 01/Sep/18 $$\mathrm{If}2\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{are}\hat{\mathrm{i}}+2\hat{\mathrm{j}}\mathrm{and}$$$$\hat{\mathrm{i}}+\hat{\mathrm{k}},\mathrm{then}\mathrm{find}\mathrm{all}\mathrm{possible}\mathrm{third}\mathrm{side}?$$ Answered by MJS last updated on…

Question Number 42521 by rahul 19 last updated on 27/Aug/18 $$\mathrm{Let}\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{c}}\mathrm{be}\mathrm{three}\mathrm{unit}\mathrm{vectors}$$$$\mathrm{such}\mathrm{that}3\overrightarrow{\mathrm{a}}+4\overrightarrow{\mathrm{b}}+5\overrightarrow{\mathrm{c}}=0.\mathrm{Then}\mathrm{prove}$$$$\mathrm{that}\:\overset{\rightarrow\:} {\mathrm{a}},\:\overset{\rightarrow} {\mathrm{b}},\overset{\rightarrow} {\mathrm{c}}\:\mathrm{are}\:\mathrm{coplanar}. \…

Question Number 42196 by rahul 19 last updated on 20/Aug/18 $$\mathrm{Let}\mathrm{P}\mathrm{be}\mathrm{an}\mathrm{interior}\mathrm{point}\mathrm{of}\mathrm{a}\mathrm{triangle}$$$$\mathrm{ABC}\mathrm{and}\mathrm{AP},\mathrm{BP},\mathrm{CP}\mathrm{meet}\mathrm{the}\mathrm{sides}\mathrm{BC},$$$$\mathrm{CA},\mathrm{AB}\mathrm{in}\mathrm{D},\mathrm{E},\mathrm{F}\mathrm{respectively}.\mathrm{Show}$$$$\mathrm{that}\frac{\mathrm{AP}}{\mathrm{PD}}=\frac{\mathrm{AF}}{\mathrm{FB}}+\frac{\mathrm{AE}}{\mathrm{EC}}.$$ Commented by rahul 19 last updated…