Use the vectors u and v to find u × (-v). $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$
A) $\mathbf { u } \times ( - \mathbf { v } ) = 47 \mathbf { i } - 55 \mathbf { j } - 48 \mathbf { k }$
B) $\mathbf { u } \times ( - \mathbf { v } ) = 55 \mathbf { i } - 55 \mathbf { j } - 48 \mathbf { k }$
C) $\mathbf { u } \times ( - \mathbf { v } ) = 47 \mathbf { i } + 47 \mathbf { j } - 48 \mathbf { k }$
D) $\mathbf { u } \times ( - \mathbf { v } ) = 55 \mathbf { i } + 47 \mathbf { j } + 48 \mathbf { k }$
E) $\mathbf { u } \times ( - \mathbf { v } ) = 48 \mathbf { i } - 55 \mathbf { j } + 47 \mathbf { k }$

Question

Use the vectors u and v to find u × (-v). $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$ 
A) $\mathbf { u } \times ( - \mathbf { v } ) = 47 \mathbf { i } - 55 \mathbf { j } - 48 \mathbf { k }$
B) $\mathbf { u } \times ( - \mathbf { v } ) = 55 \mathbf { i } - 55 \mathbf { j } - 48 \mathbf { k }$
C) $\mathbf { u } \times ( - \mathbf { v } ) = 47 \mathbf { i } + 47 \mathbf { j } - 48 \mathbf { k }$
D) $\mathbf { u } \times ( - \mathbf { v } ) = 55 \mathbf { i } + 47 \mathbf { j } + 48 \mathbf { k }$
E) $\mathbf { u } \times ( - \mathbf { v } ) = 48 \mathbf { i } - 55 \mathbf { j } + 47 \mathbf { k }$

Quizplus · Accepted Answer

The cross product $\mathbf{u} \times (-\mathbf{v})$ is found by negating vector $\mathbf{v}$ to get $-6\mathbf{i} - 6\mathbf{j} + \mathbf{k}$ and then using the determinant method or the formula for cross product. The correct calculation results in $47\mathbf{i} - 55\mathbf{j} - 48\mathbf{k}$.

Use the Vectors U and V to Find U × u=7i−j+8kv=6i+6j−k\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }u=7i−j+8kv=6i+6j−k

Use the Vectors U and V to Find U × $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$