Find the indicated cross product.
-$$\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + \mathbf { k } , \quad \mathbf { w } = 2 \mathbf { i } - 2 \mathbf { j } - \mathbf { k }$$
Find $\mathbf { w } \times \mathbf { v }$.
A) $7 \mathbf { i } + 6 \mathbf { j } + 16 \mathbf { k }$
B) $6 \mathbf { i } + 7 \mathbf { j } - 2 \mathbf { k }$
C) $- 7 \mathbf { i } - 6 \mathbf { j } - 2 \mathbf { k }$
D) $- 2 \mathbf { i } + 7 \mathbf { j } - 7 \mathbf { k }$

Question

Quizplus · Accepted Answer

The cross product $\mathbf{w} \times \mathbf{v}$ is calculated using the determinant of a matrix with unit vectors $\mathbf{i}, \mathbf{j}, \mathbf{k}$ in the first row, components of $\mathbf{w}$ in the second row, and components of $\mathbf{v}$ in the third row. The result is $-7 \mathbf{i} - 6 \mathbf{j} - 2 \mathbf{k}$.

Find the Indicated Cross Product v=4i−5j+k,w=2i−2j−k\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + \mathbf { k } , \quad \mathbf { w } = 2 \mathbf { i } - 2 \mathbf { j } - \mathbf { k }v=4i−5j+k,w=2i−2j−k

Find the Indicated Cross Product $\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + \mathbf { k } , \quad \mathbf { w } = 2 \mathbf { i } - 2 \mathbf { j } - \mathbf { k }$