Penjelasan dengan langkah-langkah:

2. Berikut cara penyelesaiannya:

2vektor a = 2(2,-1,0) = (4,-2,0)

½ (vektor b - vektor c) = ½ (4,3,2) - (2,-3,4) = (1.5,3, -1)

Maka,

2vektor a + ½ (vektor b - vektor c) = (4,-2,0) + (1.5,3,-1) = (5.5,1,-1)

Sehingga, 2vektor a + ½ (vektor b - vektor c) = (5.5,1,-1).

3. Berikut cara penyelesaiannya:

Panjang vektor a = |a| = √(3² + (-2)²) = √13

Panjang vektor b = |b| = √(1² + 5²) = √26

Panjang vektor c = |c| = √(2² + 4²) = 2√5

Maka,

3vektor a = 3(3,-2) = (9,-6)

2vektor c = 2(2,4) = (4,8)

vektor b = (1,5)

3vektor a + 2vektor c - vektor b = (9,-6) + (4,8) - (1,5) = (12,-3)

Sehingga, panjang vektor (3vektor a + 2vektor c - vektor b) = |(12,-3)| = √(12² + (-3)²) = √153.

4. Berikut cara penyelesaiannya:

3vektor a = 3(-4,0,1) = (-12,0,3)

2vektor b = 2(4,0,-1) = (8,0,-2)

Maka,

3vektor a + 2vektor b = (-12,0,3) + (8,0,-2) = (-4,0,1)

Sehingga, |3vektor a + 2vektor b| = |(-4,0,1)| = √((-4)² + 0² + 1²) = √17.