The cross product of $\mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } - 8 \mathbf { k }$ and $\mathbf { w } = \mathbf { i } + 6 \mathbf { k }$ is

A) $- 18 \mathbf { i } - 20 \mathbf { j } + 3 \mathbf { k }$
B) $18 \mathbf { i } - 20 \mathbf { j } + 3 \mathbf { k }$
C) $- 18 \mathbf { i } + 20 \mathbf { j } + 3 \mathbf { k }$
D) $18 \mathbf { i } - 20 \mathbf { j } - 3 \mathbf { k }$
E) $- 18 \mathbf { i } - 20 \mathbf { j } - 3 \mathbf { k }$

Question

The cross product of $\mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } - 8 \mathbf { k }$ and $\mathbf { w } = \mathbf { i } + 6 \mathbf { k }$ is

A) $- 18 \mathbf { i } - 20 \mathbf { j } + 3 \mathbf { k }$
B) $18 \mathbf { i } - 20 \mathbf { j } + 3 \mathbf { k }$
C) $- 18 \mathbf { i } + 20 \mathbf { j } + 3 \mathbf { k }$
D) $18 \mathbf { i } - 20 \mathbf { j } - 3 \mathbf { k }$
E) $- 18 \mathbf { i } - 20 \mathbf { j } - 3 \mathbf { k }$

Quizplus · Accepted Answer

The cross product of two vectors is a vector that is perpendicular to both of the original vectors. The direction of the cross product is determined by the right-hand rule. In this case, the cross product of $\mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } - 8 \mathbf { k }$ and $\mathbf { w } = \mathbf { i } + 6 \mathbf { k }$ is:$$\mathbf { v } \times \mathbf { w } = \begin{vmatrix} \mathbf { i } & \mathbf { j } & \mathbf { k } \\ 2 & -3 & -8 \\ 1 & 0 & 6 \end{vmatrix}$$$$= ( -18 \mathbf { i } - 20 \mathbf { j } + 3 \mathbf { k } )$$Therefore, the correct answer is A.

The Cross Product Of v=2i−3j−8k\mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } - 8 \mathbf { k }v=2i−3j−8k

The Cross Product Of $\mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } - 8 \mathbf { k }$