Use the vectors u and v to find u · (u × v). $\mathbf { u } = 6 - \mathbf { j } + 7 \mathbf { k } \quad \mathbf { v } = 5 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$
A) $\mathbf { u } ( \mathbf { u } \times \mathbf { v } ) = 10$
B) $\mathbf { u } ( \mathbf { u } \times \mathbf { v } ) = - 10$
C) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = 9$
D) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = - 9$
E) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = 0$

Question

Use the vectors u and v to find u · (u × v). $\mathbf { u } = 6 - \mathbf { j } + 7 \mathbf { k } \quad \mathbf { v } = 5 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$ 
A) $\mathbf { u } ( \mathbf { u } \times \mathbf { v } ) = 10$
B) $\mathbf { u } ( \mathbf { u } \times \mathbf { v } ) = - 10$
C) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = 9$
D) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = - 9$
E) $\mathbf { u } \cdot ( \mathbf { u } \times \mathbf { v } ) = 0$

Quizplus · Accepted Answer

The dot product of a vector with the cross product of itself and another vector is always zero due to the properties of the dot and cross products, which make the result orthogonal to the original vector.

Use the Vectors U and V to Find U · u=6−j+7kv=5i+5j−k\mathbf { u } = 6 - \mathbf { j } + 7 \mathbf { k } \quad \mathbf { v } = 5 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }u=6−j+7kv=5i+5j−k

Use the Vectors U and V to Find U · $\mathbf { u } = 6 - \mathbf { j } + 7 \mathbf { k } \quad \mathbf { v } = 5 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$