Tugas Kalkulus 2 Vektor (15521187)
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Transcript of Tugas Kalkulus 2 Vektor (15521187)
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8/18/2019 Tugas Kalkulus 2 Vektor (15521187)
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Nama : Faris Ghazi Fadlullah
NIM : 15521187
Kelas : B / Teknik Kimia
Tanggal : 31 Mare 2!1"
#$al
Diketahui : vektor´ AB = 3i – 2 j + 5k
Vektor´ AC = 2i + j – 4k
VektorB́C
= 4i – 6 j – 4k
Hitung / operasikan :
a. ´ AB + 2
B́C - 4 ´ AC
b. ´ AC - 3
´ AB + 2 B́C
. !entukan | ´ AB|
". !entukan | ´ AC +2 B́C −3 ´ AB|
%a&a'an
a. ´ AB + 2
B́C - 4 ´ AC = #3i – 2 j + 5k $ + 2#4i – 6 j – 4k $ – 4#2i
+ j – 4k $ = #3i – 2 j + 5k $ + #%i – &2 j – %k $ + #-%i – 4 j +
&6k $ = #3 – % + %$i + #-2 - &2 – 4$ j + #5 – % + &6$k = 3i – &% j – &3k
b. ´ AC - 3 ´ AB + 2 B́C = #2i + j – 4k $ – 3#3i – 2 j + 5k $ + 2#4i –
6 j – 4k $ = #2i + j – 4k $ – #'i – 6 j + 15k $ + #%i – &2 j – %k $ = #2 – ' + %$i + #& + 6 – &2$ j + #-4 – &5 – %$k = &i – 5 j – 2(k
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. | B́C | = 4i – 6 j – 4k
| B́C | = √ 42+(−6)2+(−4)2
= √ 16+36+16
= √ 68
= %)25
". | ´ AC +2 B́C −3 ´ AB| =
´ AC +2 B́C −3 ´ AB = #2i + j – 4k $ + 2#4i – 6 j – 4k $ – 3#3i – 2 j + 5k $
= #2i + j – 4k $ + #%i – &2 j – %k $ – #'i – 6 j + &5k $
= #2 + % - '$i + #& – &2 + 6$ j + #-4 – % – &5$k
=&i – 5j – 2(k
´ AC +2 B́C −3 ´ AB = √ 1
2+(−5)2+(−27)2
= √ 16+25+729
= √ 770
= 2()(5
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