Category: Vector

Question Number 79731 by M±th+et£s last updated on 27/Jan/20 Commented by M±th+et£s last updated on 27/Jan/20 $$AH:HC=4:3$$$$BG:GC=5:9$$$$findAF:FB$$ Commented by…

Question Number 13982 by tawa tawa last updated on 26/May/17 $$\mathrm{Find}\mathrm{the}\mathrm{root}\mathrm{of}\mathrm{the}\mathrm{equation}$$$${\mathrm{z}}^2-8(1-\mathrm{i})\mathrm{z}+63-16\mathrm{i}=0$$ Answered by ajfour last updated on 26/May/17 $${let}\:{z}={x}+{iy} \…

Question Number 13942 by FilupS last updated on 25/May/17 $$\mathrm{for}\mathit{v}=\left[\begin{array}{c}y\\ x\end{array}\right],\mathit{v}\in {\mathbb{R}}^2$$$$\mathit{v}\mathrm{has}\mathrm{basis}\mathrm{vectors}\hat{i}\mathrm{and}\hat{j}$$$$$$$$\mathrm{Assume}\mathrm{we}\mathrm{apply}\mathrm{a}\mathrm{basis}\mathrm{transform}\mathrm{to}$$$$\mathrm{obtain}\mathrm{new}\mathrm{basis}\mathrm{vectors}{\hat{i}}^{\prime }\mathrm{and}{\hat{j}}^{\prime }$$$$\: \…

Question Number 79131 by mathocean1 last updated on 23/Jan/20 $$\mathrm{Determine}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{points}\mathrm{M}$$$$\mathrm{such}\mathrm{as}\mid \mid \mathrm{M}\overrightarrow{\mathrm{A}}+\mathrm{M}\overrightarrow{\mathrm{B}}+2\mathrm{M}\overrightarrow{\mathrm{C}}\mid \mid =6\sqrt{3}$$$$\mathrm{AB}=\mathrm{BC}=\mathrm{AC}=6$$$$\mathrm{ABC}\mathrm{is}\mathrm{triangle}.$$ Commented by mathocean1 last…

Question Number 144166 by liberty last updated on 22/Jun/21 $$\mathrm{Given}\overrightarrow{\mathrm{p}}=\sqrt{2}\hat{\mathrm{i}}+2\sqrt{3}\hat{\mathrm{j}}+\sqrt{3}\hat{\mathrm{k}}\mathrm{\&}$$$$\:\overset{\rightarrow} {\mathrm{q}}=\mathrm{a}\:\hat {\mathrm{i}}+\hat {\mathrm{j}}\:+\mathrm{2}\hat {\mathrm{k}}\:.\:\mathrm{If}\:\mathrm{proj}_{\overset{\rightarrow} {\mathrm{q}}} \:\overset{\rightarrow} {\mathrm{p}}\:=\:\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{9}}\:\overset{\rightarrow} {\mathrm{q}}\: \…