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Question Number 73782 by liki last updated on 15/Nov/19

Commented by liki last updated on 15/Nov/19

$${I}\:{need}\:{help}\:{plz}\:{that}\:{question}\:{vector}.... \\ $$
Commented by liki last updated on 15/Nov/19

$$...{plz}\:{Mr}\:{mind}\:{is}\:{power}\:\:{i}\:{need}\:{help}\:{that}\:{qn}\:{of}\:{vector} \\ $$$$\left({a}\right),\left({b}\right)\:{and}\:\left({c}\right)\:\:{or}\:{any}\:{one}\:{to}\:{assist}\:{me}\:{plz} \\ $$
	Answered by mind is power last updated on 15/Nov/19
	$a) let A(1,1,1),B(2,3,−1) is S∣ interesection of (AB) withe plan (p) x+y+2z−5=0 AB^→ (1,2,−2) parametric equation x(t)=t+1,y(t)=2t+1,z(t)=−2t+1 S∈(p)∩(AB)⇔(t+1)+(2t+1)+2(−2t+1)=5 ⇔−t+4=5⇒t=−1⇒S(0,−1,3) b) let (d) bee this line we haven^→ (5,1,2)⊥(p)(5x+y+2z=7) ⇒vector director of d // n^→ (x,y,z)∈d⇔∃t∈R∣(x(t)=5t+1,y(t)=t+2,z(t)=2t+1} parametric equation t=y−2 ⇒ { ((x−5y+9=0)),((z−2y+3=0)) :} c)Volum=∣a^→ .(b^→ ∧c^→ )∣ b∧c=−28i^→ +30j^→ +6k^→ ∣a^→ .(b∧c)∣=∣2.−28+4.30+6.1∣=70 ua^3$
	$$\left.\mathrm{a}\right)\:\mathrm{let}\:\mathrm{A}\left(\mathrm{1},\mathrm{1},\mathrm{1}\right),\mathrm{B}\left(\mathrm{2},\mathrm{3},−\mathrm{1}\right) \\ $$$$\mathrm{is}\:\mathrm{S}\mid\:\mathrm{interesection}\:\mathrm{of}\:\left(\mathrm{AB}\right)\:\mathrm{withe}\:\mathrm{plan}\:\left(\mathrm{p}\right)\:\mathrm{x}+\mathrm{y}+\mathrm{2z}−\mathrm{5}=\mathrm{0} \\ $$$$\mathrm{A}\overset{\rightarrow} {\mathrm{B}}\left(\mathrm{1},\mathrm{2},−\mathrm{2}\right) \\ $$$$\mathrm{parametric}\:\mathrm{equation} \\ $$$$\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}+\mathrm{1},\mathrm{y}\left(\mathrm{t}\right)=\mathrm{2t}+\mathrm{1},\mathrm{z}\left(\mathrm{t}\right)=−\mathrm{2t}+\mathrm{1} \\ $$$$\mathrm{S}\in\left(\mathrm{p}\right)\cap\left(\mathrm{AB}\right)\Leftrightarrow\left(\mathrm{t}+\mathrm{1}\right)+\left(\mathrm{2t}+\mathrm{1}\right)+\mathrm{2}\left(−\mathrm{2t}+\mathrm{1}\right)=\mathrm{5} \\ $$$$\Leftrightarrow−\mathrm{t}+\mathrm{4}=\mathrm{5}\Rightarrow\mathrm{t}=−\mathrm{1}\Rightarrow\mathrm{S}\left(\mathrm{0},−\mathrm{1},\mathrm{3}\right) \\ $$$$\left.\mathrm{b}\right)\:\mathrm{let}\:\:\left(\mathrm{d}\right)\:\mathrm{bee}\:\mathrm{this}\:\mathrm{line}\:\mathrm{we}\:\mathrm{have}\overset{\rightarrow} {\mathrm{n}}\left(\mathrm{5},\mathrm{1},\mathrm{2}\right)\bot\left(\mathrm{p}\right)\left(\mathrm{5x}+\mathrm{y}+\mathrm{2z}=\mathrm{7}\right) \\ $$$$\Rightarrow\mathrm{vector}\:\:\mathrm{director}\:\mathrm{of}\:\mathrm{d}\://\:\overset{\rightarrow} {\mathrm{n}} \\ $$$$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\in\mathrm{d}\Leftrightarrow\exists\mathrm{t}\in\mathbb{R}\mid\left(\mathrm{x}\left(\mathrm{t}\right)=\mathrm{5t}+\mathrm{1},\mathrm{y}\left(\mathrm{t}\right)=\mathrm{t}+\mathrm{2},\mathrm{z}\left(\mathrm{t}\right)=\mathrm{2t}+\mathrm{1}\right\} \\ $$$$\mathrm{parametric}\:\mathrm{equation} \\ $$$$\mathrm{t}=\mathrm{y}−\mathrm{2}\:\Rightarrow\begin{cases}{\mathrm{x}−\mathrm{5y}+\mathrm{9}=\mathrm{0}}\\{\mathrm{z}−\mathrm{2y}+\mathrm{3}=\mathrm{0}}\end{cases}\:\: \\ $$$$\left.\mathrm{c}\right)\mathrm{Volum}=\mid\overset{\rightarrow} {\mathrm{a}}.\left(\overset{\rightarrow} {\mathrm{b}}\wedge\overset{\rightarrow} {\mathrm{c}}\right)\mid \\ $$$$\mathrm{b}\wedge\mathrm{c}=−\mathrm{28}\overset{\rightarrow} {\mathrm{i}}+\mathrm{30}\overset{\rightarrow} {\mathrm{j}}+\mathrm{6}\overset{\rightarrow} {\mathrm{k}} \\ $$$$\mid\overset{\rightarrow} {\mathrm{a}}.\left(\mathrm{b}\wedge\mathrm{c}\right)\mid=\mid\mathrm{2}.−\mathrm{28}+\mathrm{4}.\mathrm{30}+\mathrm{6}.\mathrm{1}\mid=\mathrm{70}\:\:\mathrm{ua}^{\mathrm{3}} \\ $$$$ \\ $$
	Commented by liki last updated on 15/Nov/19

	$$...{Thanks}\:{very}\:{much}\:{sir}\:{i}\:{appriciate}\:{your}\:{work}! \\ $$
	Commented by mind is power last updated on 15/Nov/19

	$$\mathrm{y}'\mathrm{re}\:\mathrm{welcom} \\ $$
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