JAWABAN 1731130078 KARINA AYU DEWANTI
Jawaban dari soal 1
A = i + √2j + √5k
B = i - √2j + √5k
A dan B = 1 + 1 + √2 + (√-2) + √5 + √5
= 1 - 2 + 5
= 4
|A| = √(12+(√2)2 + (√5)2)
= √8
Sudut antara A dan B
cos ∅ = A . B / |A| . |B|
= 4 / (√8 . √8)
= 4 / 8
= 1 / 2
sudut ∅ 1/2 = 60 derajat
Jawaban dari soal 2
A = 8i + 6j
B = 2i + 10j + 8k
C = 2i + 3j + k
|A-BxC|
BxC = (2i + 10j + 8k) x (2i + 3j + k)
= (2i x 3j) + (2i x k) + (10j x 2i) + (10j x k) + (8k x 2i) + (8k x 3j)
= 6k + (-2j) + (-20k) + 10i + 16j + (-24i)
= (-14i) + 14j - 14k
|A-(BxC) = (8i + 6j) - ((-14i) + 14j - 14k)
= 22i - 8j + 14k
A-(BxC) = √22² - 8² + 14²
= √484-64+196
= √616
= 24,82
A = i + √2j + √5k
B = i - √2j + √5k
A dan B = 1 + 1 + √2 + (√-2) + √5 + √5
= 1 - 2 + 5
= 4
|A| = √(12+(√2)2 + (√5)2)
= √8
Sudut antara A dan B
cos ∅ = A . B / |A| . |B|
= 4 / (√8 . √8)
= 4 / 8
= 1 / 2
sudut ∅ 1/2 = 60 derajat
Jawaban dari soal 2
A = 8i + 6j
B = 2i + 10j + 8k
C = 2i + 3j + k
|A-BxC|
BxC = (2i + 10j + 8k) x (2i + 3j + k)
= (2i x 3j) + (2i x k) + (10j x 2i) + (10j x k) + (8k x 2i) + (8k x 3j)
= 6k + (-2j) + (-20k) + 10i + 16j + (-24i)
= (-14i) + 14j - 14k
|A-(BxC) = (8i + 6j) - ((-14i) + 14j - 14k)
= 22i - 8j + 14k
A-(BxC) = √22² - 8² + 14²
= √484-64+196
= √616
= 24,82