Question

Jika vektor a = xi - 4j + 8k tegak lurus vektor b = 2xi + 2xj - 3k, maka nilai x positif. maka a + b adalah...


tolong sama cara penyelesaian detailnya ya ^^

Answer 1

Vektor tegak lurus, maka dot product = 0

a.b = 0
(xi - 4j + 8k).(2xi + 2xj - 3k) = 0
(x.2x) + (-4.2x) + (8.-3) = 0
2x^2 - 8x - 24 = 0
x^2 - 4x - 12 = 0
(x - 6)(x + 2) = 0

x = 6 atau x = -2

karena x positif, maka x = 6

a = 6i - 4k + 8k
b = 12i + 12j - 3k

a + b = (6 + 12)i + (-4 + 12)j + (8 - 3)k
= 18i + 8j + 5k