Komponen vektor PQ = Q - P
= (8-6)i + (-x -x)j + (2-3)k
= 2i + (-2x)j + (-1)k
= 2i - 2xj - k
Panjang vektor PQ = √(x² + y² + z²)
3 = √[(2²) + (-2x)² + (-1)²]
3 = √(4 + 4x² + 1)
3 = √(4x² + 5)
3² = [√(4x² + 5)]²
9 = 4x² + 5
0 = 4x² + 5 - 9
0 = 4x² - 4
0 = (2x)² - 2²
0 = (2x + 2)(2x - 2)
↓
2x + 2 = 0 2x - 2 = 0
2x = -2 2x = 2
x1 = -1 x2 = 1
Karena yang dicari x positif, maka jawabannya adalah D.
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Komponen vektor PQ = Q - P
= (8-6)i + (-x -x)j + (2-3)k
= 2i + (-2x)j + (-1)k
= 2i - 2xj - k
Panjang vektor PQ = √(x² + y² + z²)
3 = √[(2²) + (-2x)² + (-1)²]
3 = √(4 + 4x² + 1)
3 = √(4x² + 5)
3² = [√(4x² + 5)]²
9 = 4x² + 5
0 = 4x² + 5 - 9
0 = 4x² - 4
0 = (2x)² - 2²
0 = (2x + 2)(2x - 2)
↓
2x + 2 = 0 2x - 2 = 0
2x = -2 2x = 2
x1 = -1 x2 = 1
Karena yang dicari x positif, maka jawabannya adalah D.