IBHardVectors10–12

Vector Cross Product

Produto Vetorial

Find the cross product of $\vec{a} = (1, 2, 3)$ and $\vec{b} = (4, 5, 6)$ . What is the area of the parallelogram formed by these vectors?

$\vec{a} \times \vec{b} = (a_2b_3 - a_3b_2, a_3b_1 - a_1b_3, a_1b_2 - a_2b_1)$ . Area $= |\vec{a} \times \vec{b}|$ .

Solution

Step 1 of 4

1. $\vec{a} \times \vec{b} = (2 \cdot 6 - 3 \cdot 5, 3 \cdot 4 - 1 \cdot 6, 1 \cdot 5 - 2 \cdot 4)$