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Question-119013

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Question Number 119013 by zakirullah last updated on 21/Oct/20
Commented by zakirullah last updated on 21/Oct/20
find the component and the magnitude of PQ^→ i. P(−1,2), Q(2,−1) ii. P(−2,1), Q(2,3) iii. P(−1,1,2), Q(2,−1,3) iv. P(2,4,6), Q(1,−2,3)
$$\:\:\:\:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{component}}\:\boldsymbol{{and}}\: \\ $$$$\:\:\:\:\:\:\boldsymbol{{the}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{P}}\overset{\rightarrow} {\boldsymbol{{Q}}} \\ $$$${i}.\:\:\boldsymbol{{P}}\left(−\mathrm{1},\mathrm{2}\right),\:\boldsymbol{{Q}}\left(\mathrm{2},−\mathrm{1}\right) \\ $$$${ii}.\:\:\boldsymbol{{P}}\left(−\mathrm{2},\mathrm{1}\right),\:\boldsymbol{{Q}}\left(\mathrm{2},\mathrm{3}\right) \\ $$$${iii}.\:\:\boldsymbol{{P}}\left(−\mathrm{1},\mathrm{1},\mathrm{2}\right),\:\boldsymbol{{Q}}\left(\mathrm{2},−\mathrm{1},\mathrm{3}\right) \\ $$$${iv}.\:\:\boldsymbol{{P}}\left(\mathrm{2},\mathrm{4},\mathrm{6}\right),\:\:\boldsymbol{{Q}}\left(\mathrm{1},−\mathrm{2},\mathrm{3}\right) \\ $$
Answered by ebi last updated on 21/Oct/20
point P(p_1 ,p_2 ,...,p_n ), Q(q_1 ,q_2 ,...,q_n ) component, PQ^→ =⟨q_1 −p_1 ,q_2 −p_1 ,...,q_n −p_n ⟩=⟨u_1 ,u_2 ,...,u_n ⟩ magnitude,∣∣PQ^→ ∣∣=(√(u_1 ^2 +u_2 ^2 +...+u_n ^2 )) i) PQ^→ =⟨3,−3⟩, ∣∣PQ^→ ∣∣=3(√2) ii) PQ^→ =⟨4,2⟩, ∣∣PQ^→ ∣∣=2(√5) iii) PQ^→ =⟨3,−2,1⟩, ∣∣PQ^→ ∣∣=(√(14)) iv) PQ^→ =⟨−1,−6,−3⟩, ∣∣PQ^→ ∣∣=(√(46))
$${point}\:{P}\left({p}_{\mathrm{1}} ,{p}_{\mathrm{2}} ,…,{p}_{{n}} \right),\:{Q}\left({q}_{\mathrm{1}} ,{q}_{\mathrm{2}} ,…,{q}_{{n}} \right) \\ $$$${component},\:{P}\overset{\rightarrow} {{Q}}=\langle{q}_{\mathrm{1}} −{p}_{\mathrm{1}} ,{q}_{\mathrm{2}} −{p}_{\mathrm{1}} ,…,{q}_{{n}} −{p}_{{n}} \rangle=\langle{u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,…,{u}_{{n}} \rangle \\ $$$${magnitude},\mid\mid{P}\overset{\rightarrow} {{Q}}\mid\mid=\sqrt{{u}_{\mathrm{1}} ^{\mathrm{2}} +{u}_{\mathrm{2}} ^{\mathrm{2}} +…+{u}_{{n}} ^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.{i}\right) \\ $$$${P}\overset{\rightarrow} {{Q}}=\langle\mathrm{3},−\mathrm{3}\rangle,\:\:\:\mid\mid{P}\overset{\rightarrow} {{Q}}\mid\mid=\mathrm{3}\sqrt{\mathrm{2}} \\ $$$$ \\ $$$$\left.{ii}\right) \\ $$$${P}\overset{\rightarrow} {{Q}}=\langle\mathrm{4},\mathrm{2}\rangle,\:\:\:\mid\mid{P}\overset{\rightarrow} {{Q}}\mid\mid=\mathrm{2}\sqrt{\mathrm{5}} \\ $$$$ \\ $$$$\left.{iii}\right) \\ $$$${P}\overset{\rightarrow} {{Q}}=\langle\mathrm{3},−\mathrm{2},\mathrm{1}\rangle,\:\:\:\mid\mid{P}\overset{\rightarrow} {{Q}}\mid\mid=\sqrt{\mathrm{14}} \\ $$$$ \\ $$$$\left.{iv}\right) \\ $$$${P}\overset{\rightarrow} {{Q}}=\langle−\mathrm{1},−\mathrm{6},−\mathrm{3}\rangle,\:\:\:\mid\mid{P}\overset{\rightarrow} {{Q}}\mid\mid=\sqrt{\mathrm{46}} \\ $$$$ \\ $$
Commented by zakirullah last updated on 21/Oct/20
thanks sir
$$\boldsymbol{{thanks}}\:\boldsymbol{{sir}} \\ $$

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