Question

problem 11
(fill in the blank) : given the vectors,
\\(\vec{v} = \hat{i} + 2\hat{j} - \hat{k}\\)
and
\\(\vec{w} = -2\hat{i} + 3\hat{j} - \hat{k}\\),
please calculate the cross product \\(\vec{v} \times \vec{w}\\).
\\(\vec{v} \times \vec{w} = <\text{your answer here}>\\)

Explanation:

Step1: Set up cross product determinant

$$\vec{v} \times \vec{w} =
LATEXBLOCK0
$$

Step2: Expand along first row

$$\hat{i}(2(-1) - (-1)(3)) - \hat{j}(1(-1) - (-1)(-2)) + \hat{k}(1(3) - 2(-2))$$

Step3: Compute each component

$\hat{i}(-2 + 3) - \hat{j}(-1 - 2) + \hat{k}(3 + 4)$

Step4: Simplify components

$\hat{i}(1) - \hat{j}(-3) + \hat{k}(7)$

Answer:

$\hat{i} + 3\hat{j} + 7\hat{k}$ (or $\langle 1, 3, 7
angle$)