### ASSIGNMENT C

1. If [tex]\( \mathbf{A} = i - 2j - 3k \)[/tex], [tex]\( \mathbf{B} = 2i + j - k \)[/tex], and [tex]\( \mathbf{C} = i + 3j - 2k \)[/tex], find:

(a) [tex]\( | (\mathbf{A} \times \mathbf{B}) \times \mathbf{C} | \)[/tex]

(b) [tex]\( | \mathbf{A} \times (\mathbf{B} \times \mathbf{C}) | \)[/tex]

(c) [tex]\( \mathbf{A} \cdot (\mathbf{B} \times \mathbf{C}) \)[/tex]

(d) [tex]\( (\mathbf{A} \times \mathbf{B}) \cdot \mathbf{C} \)[/tex]

(e) [tex]\( (\mathbf{A} \times \mathbf{B}) \times (\mathbf{B} \times \mathbf{C}) \)[/tex]

(f) [tex]\( (\mathbf{A} \times \mathbf{B})(\mathbf{B} \cdot \mathbf{C}) \)[/tex]

2. Find the area of a parallelogram having diagonals [tex]\( \mathbf{A} = 3i + j - 2k \)[/tex] and [tex]\( \mathbf{B} = i - 3j + 4k \)[/tex].

Answer: [tex]\( 5 \sqrt{3} \)[/tex]

3. Find the area of a triangle with vertices at [tex]\( (3, -1, 2) \)[/tex], [tex]\( (1, -1, -3) \)[/tex], and [tex]\( (4, -3, 1) \)[/tex].