JAWABAN 1731130007 YUSDISTIRAWAN ALDO
jawaban dari soal 1 :
jawaban dari soal 2 :
1. Hasil perkalian dot :
i.i = j.j = k.k = 1
= A.B = (2i - 4j + k).(3i + 2j - 3k)
= ( 2i.3i + 2i.2j - 2i.3k - 4j.3i - 4j.2j + 4j.3k + k.3i + k.2j – k.3k )
= ( 6 + 0 - 0 - 0 - 8 + 0 + 0 + 0 – 3)
= (8 - 8 - 3)
= -3
Hasil perkalian silang :
i X i = j X j = k X k = 1
i X j = k j X i = -k
j X k = i k X j = -i
k X i = j k X i = -j
= A X B = (2i - 4j + k).(3i + 2j - 3k)
= ( (2.3)i X i + (2.2)i X j - (2.3)i X k - (4.3)j X i - (4.2)j X j + (4.3)j X k + (1.3)k X i + (1.2)k X j – (1.3)k X k )
= 8.(0) + 4k + 6j + 12k – 8.(0) + 12i + 3j – 2i – 9.(0)
= + 4k + 12k + 6j + 3j + 12i – 2i
= 10i + 9j + 16k
jawaban dari soal 2 :
2. diket A = 9i + 2j
B = i – 10j – 3k
Tentukan : A X B
Jawab :
i X i = j X j = k X k = 1
i X j = k j X i = -k
j X k = i k X j = -i
k X i = j k X i = -j
= A X B = (9i + 2j) X (i – 10j – 3k)
= ( (9.1)i X i - (9.10)i X j - (9.3)i X k + (2.1)j X i - (2.10)j X j - (2.3)j X k)
= 9.(0) - 90k + 27j - 2k – 20.(0) - 6i
= - 90k – 2k + 27j – 6i
= -6i + 27k – 92k