Diketahui a = 3i- 6j + xk dan b = 2i-6j. Jika | | = 9. Tentukan |2a-b|

Langkah 1 : Calculate the magnitude of vector a: Given a = 3i - 6j + xk, the magnitude of a is ||a|| = sqrt((3)^2 + (-6)^2 + x^2) = sqrt(9 + 36 + x^2) = sqrt(45 + x^2). Langkah 2 : Given that ||a|| = 9, we can set up the equation: sqrt(45 + x^2) = 9. Langkah 3 : Solve for x in the equation: 45 + x^2 = 81, x^2 = 81 - 45, x^2 = 36, x = 6 or x = -6. Langkah 4 : Substitute the value of x back into vector a: If x = 6, then a = 3i - 6j + 6k. If x = -6, then a = 3i - 6j - 6k. Langkah 5 : Calculate 2a - b: If x = 6, then 2a - b = 2(3i - 6j + 6k) - (2i - 6j) = 6i - 12j + 12k - 2i + 6j = 4i - 6j + 12k. If x = -6, then 2a - b = 2(3i - 6j - 6k) - (2i - 6j) = 6i - 12j - 12k - 2i + 6j = 4i - 6j - 12k. Langkah 6 : Calculate the magnitude of 2a - b: ||2a - b|| = sqrt((4)^2 + (-6)^2 + (12)^2) = sqrt(16 + 36 + 144) = sqrt(196) = 14. Jawaban akhir : 14