Find the indicated cross product.
-$$\mathbf { v } = 6 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k } , \quad \mathbf { w } = - 4 \mathbf { i } - 4 \mathbf { k }$$
Find $v \times w$.
A) $- 20 \mathbf { i } + 12 \mathrm { j } - 20 \mathbf { k }$
B) $- 20 \mathbf { i } + 36 \mathbf { j } + 20 \mathbf { k }$
C) $- 15 i + 34 j + 30 k$
D) $20 \mathrm { i } + 20 \mathrm { j } - 36 \mathbf { k }$

Question

Quizplus · Accepted Answer

To find the cross product $v \times w$, we use the determinant of a 3x3 matrix with the unit vectors $\mathbf{i}, \mathbf{j}, \mathbf{k}$ in the first row, the components of $\mathbf{v}$ in the second row, and the components of $\mathbf{w}$ in the third row. Calculating this determinant gives us $-20\mathbf{i} + 36\mathbf{j} + 20\mathbf{k}$.

Find the Indicated Cross Product v=6i+5j−3k,w=−4i−4k\mathbf { v } = 6 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k } , \quad \mathbf { w } = - 4 \mathbf { i } - 4 \mathbf { k }v=6i+5j−3k,w=−4i−4k

Find the Indicated Cross Product $\mathbf { v } = 6 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k } , \quad \mathbf { w } = - 4 \mathbf { i } - 4 \mathbf { k }$