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


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Question Number 119184 by Attila last updated on 22/Oct/20

$N a m a : A t t i l a A b i e m F a r h a n$ $K e l a s : X I B K P$ $T u g a s K D 3.18 M T K$ $1 . j a w a b :$ $\vec{u} = (\begin{matrix} - 3 \\ - 4 \\ 12 \end{matrix})$ $∣ \vec{u} ∣= \sqrt{(- 3^{2}) + {(- 4)}^{2} + 12^{2}}$ $= \sqrt{9 + 16 + 144}$ $= \sqrt{169} = 13$ $2 . j a w a b :$ $\vec{a} = (\begin{matrix} 2 \\ - 1 \\ 3 \end{matrix}) \vec{b} = (\begin{matrix} 7 \\ 13 \\ 5 \end{matrix})$ $\vec{a} + \vec{b} = (\begin{matrix} 9 \\ 12 \\ 8 \end{matrix})$ $∣ \vec{a} + \vec{b} ∣= \sqrt{9^{2} + 12^{2} + 8^{2}}$ $= \sqrt{81 + 144 + 64}$ $= \sqrt{289}$ $3 . j a w a b$ $\vec{u} = (\begin{matrix} 7 \\ 9 \\ - 17 \end{matrix}) \vec{v} = (\begin{matrix} - 2 \\ - 3 \\ 19 \end{matrix})$ $\vec{u} - \vec{v} = (\begin{matrix} 9 \\ 12 \\ 36 \end{matrix})$ $∣ \vec{u} + \vec{v} ∣= \sqrt{9^{2} + 12^{2} + 36^{2}}$ $= \sqrt{81 + 144 + 1296}$ $= \sqrt{1521}$ $4 . j a w a b :$ $A . 2 \vec{a} = (\begin{matrix} - 6 \\ - 8 \\ - 24 \end{matrix})$ $∣ 2 \vec{a} ∣= \sqrt{{(- 6)}^{2} + {(- 8)}^{2} + {(- 24)}^{2}}$ $= \sqrt{36 + 64 + 576}$ $= \sqrt{676}$ $= 26$ $\frac{1}{2} \vec{b} = (\begin{matrix} 3 \\ 4 \\ 12 \end{matrix})$ $∣ \frac{1}{2} \vec{b} ∣= \sqrt{3^{2} + 4^{2} + 12^{2}} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$ $B . 4 \vec{a} + \vec{b} = (\begin{matrix} - 12 \\ - 16 \\ - 48 \end{matrix}) + (\begin{matrix} 6 \\ 8 \\ 24 \end{matrix}) = (\begin{matrix} - 6 \\ - 8 \\ - 24 \end{matrix})$ $∣ 4 \vec{a} + \vec{b} ∣= \sqrt{{(- 6)}^{2} + {(- 8)}^{2} + {(- 24)}^{2}}$ $= \sqrt{36 + 64 + 576}$ $= \sqrt{676} = 26$ $5 . j a w a b :$ $\vec{u} = 8 i + 3 k$ $\vec{v} = 5 j - 9 k$ $\vec{u} . \vec{v} = (8.0) i + (0.5) j + (3 . - 9) k$ $= 0 + 0 - 27 k$ $\vec{u} . \vec{v} = - 27 k$
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