QuestionIf $\mathbf{a}=\mathbf{i}+\mathbf{j}+3 \mathbf{k}$ and $\mathbf{b}=\mathbf{i}+\mathbf{j}+3 \mathbf{k}$ Compute the cross product $\mathbf{a} \times \mathbf{b}$. $$\mathbf{a} \times \mathbf{b}=\square \mathrm{i}+\square \mathrm{j}+\square \mathrm{k}$$

Studdy Solution
Apply the cross product formula to vectors $\mathbf{a}$ and $\mathbf{b}$:
Since $\mathbf{a} = \mathbf{b}$, the cross product $\mathbf{a} \times \mathbf{b}$ is:
$\mathbf{a} \times \mathbf{b} = (1 \cdot 3 - 3 \cdot 1) \mathbf{i} - (1 \cdot 3 - 3 \cdot 1) \mathbf{j} + (1 \cdot 1 - 1 \cdot 1) \mathbf{k}$
Simplifying each term:
$= (3 - 3) \mathbf{i} - (3 - 3) \mathbf{j} + (1 - 1) \mathbf{k}$
$= 0 \mathbf{i} + 0 \mathbf{j} + 0 \mathbf{k}$
The cross product $\mathbf{a} \times \mathbf{b}$ is:
$\boxed{0 \mathbf{i} + 0 \mathbf{j} + 0 \mathbf{k}}$