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Nama-Attila-Abiem-Farhan-Kelas-XI-BKP-Tugas-KD-3-18-MTK-1-jawab-u-3-4-12-u-3-2-4-2-12-2-9-16-144-169-13-2-jawab-a-2-




Question Number 119184 by Attila last updated on 22/Oct/20
Nama : Attila Abiem Farhan  Kelas : XI BKP  Tugas KD 3.18 MTK  1. jawab :   u^→ = (((−3)),((−4)),((  12)) )   ∣u^→ ∣=(√((−3^2 )+(−4)^2 +12^2 ))        =(√(9+16+144))        =(√(169))=13  2. jawab :  a^→ = ((2),((−1)),(3) ) b^→ = ((7),((13)),(5) )   a^→ +b^→ = ((9),((12)),(8) )  ∣a^→ +b^→ ∣=(√(9^2 +12^2 +8^2 ))                =(√(81+144+64))                =(√(289))  3. jawab  u^→ = ((7),(9),((−17)) ) v^→ = (((−2)),((−3)),((19)) )  u^→ −v^→ = ((9),((12)),((36)) )  ∣u^→ +v^→ ∣=(√(9^2 +12^2 +36^2 ))                =(√(81+144+1296))                =(√(1521))  4. jawab :   A.   2a^→ = (((−6)),((−8)),((−24)) )          ∣2a^→ ∣=(√((−6)^2 +(−8)^2 +(−24)^2 ))                  =(√(36+64+576))                  =(√(676))                  =26          (1/2)b^→ = ((3),(4),((12)) )         ∣(1/2)b^→ ∣=(√(3^2 +4^2 +12^2 ))=(√(9+16+144))=(√(169))=13    B.    4a^→ +b^→ = (((−12)),((−16)),((−48)) ) + ((6),(8),((24)) ) =  (((−6)),((−8)),((−24)) )          ∣4a^→ +b^→ ∣=(√((−6)^2 +(−8)^2 +(−24)^2 ))                          =(√(36+64+576))                          =(√(676))=26  5. jawab :   u^→ =8i+3k  v^→ =5j−9k  u^→ .v^→ =(8.0)i+(0.5)j+(3.−9)k          =0+0−27k  u^→ .v^→ =−27k
$${Nama}\::\:{Attila}\:{Abiem}\:{Farhan} \\ $$$${Kelas}\::\:{XI}\:{BKP} \\ $$$${Tugas}\:{KD}\:\mathrm{3}.\mathrm{18}\:{MTK} \\ $$$$\mathrm{1}.\:{jawab}\:: \\ $$$$\:\overset{\rightarrow} {{u}}=\begin{pmatrix}{−\mathrm{3}}\\{−\mathrm{4}}\\{\:\:\mathrm{12}}\end{pmatrix}\: \\ $$$$\mid\overset{\rightarrow} {{u}}\mid=\sqrt{\left(−\mathrm{3}^{\mathrm{2}} \right)+\left(−\mathrm{4}\right)^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:=\sqrt{\mathrm{9}+\mathrm{16}+\mathrm{144}} \\ $$$$\:\:\:\:\:\:=\sqrt{\mathrm{169}}=\mathrm{13} \\ $$$$\mathrm{2}.\:{jawab}\:: \\ $$$$\overset{\rightarrow} {{a}}=\begin{pmatrix}{\mathrm{2}}\\{−\mathrm{1}}\\{\mathrm{3}}\end{pmatrix}\:\overset{\rightarrow} {{b}}=\begin{pmatrix}{\mathrm{7}}\\{\mathrm{13}}\\{\mathrm{5}}\end{pmatrix}\: \\ $$$$\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}=\begin{pmatrix}{\mathrm{9}}\\{\mathrm{12}}\\{\mathrm{8}}\end{pmatrix} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=\sqrt{\mathrm{9}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} +\mathrm{8}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{81}+\mathrm{144}+\mathrm{64}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{289}} \\ $$$$\mathrm{3}.\:{jawab} \\ $$$$\overset{\rightarrow} {{u}}=\begin{pmatrix}{\mathrm{7}}\\{\mathrm{9}}\\{−\mathrm{17}}\end{pmatrix}\:\overset{\rightarrow} {{v}}=\begin{pmatrix}{−\mathrm{2}}\\{−\mathrm{3}}\\{\mathrm{19}}\end{pmatrix} \\ $$$$\overset{\rightarrow} {{u}}−\overset{\rightarrow} {{v}}=\begin{pmatrix}{\mathrm{9}}\\{\mathrm{12}}\\{\mathrm{36}}\end{pmatrix} \\ $$$$\mid\overset{\rightarrow} {{u}}+\overset{\rightarrow} {{v}}\mid=\sqrt{\mathrm{9}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} +\mathrm{36}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{81}+\mathrm{144}+\mathrm{1296}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{1521}} \\ $$$$\mathrm{4}.\:{jawab}\::\: \\ $$$${A}.\:\:\:\mathrm{2}\overset{\rightarrow} {{a}}=\begin{pmatrix}{−\mathrm{6}}\\{−\mathrm{8}}\\{−\mathrm{24}}\end{pmatrix}\: \\ $$$$\:\:\:\:\:\:\:\mid\mathrm{2}\overset{\rightarrow} {{a}}\mid=\sqrt{\left(−\mathrm{6}\right)^{\mathrm{2}} +\left(−\mathrm{8}\right)^{\mathrm{2}} +\left(−\mathrm{24}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{36}+\mathrm{64}+\mathrm{576}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{676}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{26} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\overset{\rightarrow} {{b}}=\begin{pmatrix}{\mathrm{3}}\\{\mathrm{4}}\\{\mathrm{12}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\mid\frac{\mathrm{1}}{\mathrm{2}}\overset{\rightarrow} {{b}}\mid=\sqrt{\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} }=\sqrt{\mathrm{9}+\mathrm{16}+\mathrm{144}}=\sqrt{\mathrm{169}}=\mathrm{13} \\ $$$$ \\ $$$${B}.\:\:\:\:\mathrm{4}\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}=\begin{pmatrix}{−\mathrm{12}}\\{−\mathrm{16}}\\{−\mathrm{48}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{6}}\\{\mathrm{8}}\\{\mathrm{24}}\end{pmatrix}\:=\:\begin{pmatrix}{−\mathrm{6}}\\{−\mathrm{8}}\\{−\mathrm{24}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\mid\mathrm{4}\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=\sqrt{\left(−\mathrm{6}\right)^{\mathrm{2}} +\left(−\mathrm{8}\right)^{\mathrm{2}} +\left(−\mathrm{24}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{36}+\mathrm{64}+\mathrm{576}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{676}}=\mathrm{26} \\ $$$$\mathrm{5}.\:{jawab}\::\: \\ $$$$\overset{\rightarrow} {{u}}=\mathrm{8}{i}+\mathrm{3}{k} \\ $$$$\overset{\rightarrow} {{v}}=\mathrm{5}{j}−\mathrm{9}{k} \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=\left(\mathrm{8}.\mathrm{0}\right){i}+\left(\mathrm{0}.\mathrm{5}\right){j}+\left(\mathrm{3}.−\mathrm{9}\right)\mathrm{k} \\ $$$$\:\:\:\:\:\:\:\:=\mathrm{0}+\mathrm{0}−\mathrm{27}{k} \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=−\mathrm{27}{k} \\ $$

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