Use the vectors u and v to find v × u. $\mathbf { u } = 3 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } \quad \mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }$
A) $\mathbf { v } \times \mathbf { u } = 11 \mathbf { i } + 7 \mathbf { j } - 8 \mathbf { k }$
B) $\mathbf { v } \times \mathbf { u } = 7 \mathbf { i } - 11 \mathbf { j } - 8 \mathbf { k }$
C) $\mathbf { v } \times \mathbf { u } = - 7 \mathbf { i } + 11 \mathbf { j } + 7 \mathbf { k }$
D) $\mathbf { v } \times \mathbf { u } = 11 \mathbf { i } + 11 \mathbf { j } + 8 \mathbf { k }$
E) $\mathbf { v } \times \mathbf { u } = 7 \mathbf { i } - 8 \mathbf { j } + 8 \mathbf { k }$

Question

Use the vectors u and v to find v × u.  $\mathbf { u } = 3 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } \quad \mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }$ 
A) $\mathbf { v } \times \mathbf { u } = 11 \mathbf { i } + 7 \mathbf { j } - 8 \mathbf { k }$
B) $\mathbf { v } \times \mathbf { u } = 7 \mathbf { i } - 11 \mathbf { j } - 8 \mathbf { k }$
C) $\mathbf { v } \times \mathbf { u } = - 7 \mathbf { i } + 11 \mathbf { j } + 7 \mathbf { k }$
D) $\mathbf { v } \times \mathbf { u } = 11 \mathbf { i } + 11 \mathbf { j } + 8 \mathbf { k }$
E) $\mathbf { v } \times \mathbf { u } = 7 \mathbf { i } - 8 \mathbf { j } + 8 \mathbf { k }$

Quizplus · Accepted Answer

The cross product $ \mathbf{v} \times \mathbf{u} $ is calculated using the determinant of a matrix formed by 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{u} $ in the third row. The correct calculation results in $ 7 \mathbf{i} - 11 \mathbf{j} - 8 \mathbf{k} $.

Use the Vectors U and V to Find V × u=3i−j+4kv=2i+2j−k\mathbf { u } = 3 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } \quad \mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }u=3i−j+4kv=2i+2j−k

Use the Vectors U and V to Find V × $\mathbf { u } = 3 \mathbf { i } - \mathbf { j } + 4 \mathbf { k } \quad \mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }$