Use the given vectors to find the indicated expression.
-$$\mathbf { v } = - 3 \mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k } , \quad \mathbf { w } = 2 \mathbf { i } + 4 \mathbf { j } - 2 \mathbf { k } , \quad \mathbf { u } = - 4 \mathbf { i } - 4 \mathbf { j } - 3 \mathbf { k }$$
Find $\mathbf { v } \cdot ( \mathbf { v } \times \mathbf { w } )$.
A) 90
B) 0
C) $- 90$
D) 130

Question

Quizplus · Accepted Answer

The dot product of a vector with the cross product of itself and another vector is always zero because the cross product is perpendicular to the original vector, making their dot product zero.

Use the Given Vectors to Find the Indicated Expression Find v⋅(v×w)\mathbf { v } \cdot ( \mathbf { v } \times \mathbf { w } )v⋅(v×w)

Use the Given Vectors to Find the Indicated Expression Find $\mathbf { v } \cdot ( \mathbf { v } \times \mathbf { w } )$