$\text { Given } \mathbf { u } = ( 8,3,3 \} \text { and } \mathbf { v } = \{ 2 , - 1,5 \} \text { find } \mathbf { u } \times \mathbf { v }$
A) $\{ 29 , - 22,6 \}$
B) $( - 18 , - 68 , - 14 )$
C) $( 18 , - 34 , - 14 )$
D) $( - 18,34,14 )$
E) $( 37 , - 34 , - 27 )$

Question

$\text { Given } \mathbf { u } = ( 8,3,3 \} \text { and } \mathbf { v } = \{ 2 , - 1,5 \} \text { find } \mathbf { u } \times \mathbf { v }$ 
A) $\{ 29 , - 22,6 \}$
B) $( - 18 , - 68 , - 14 )$
C) $( 18 , - 34 , - 14 )$
D) $( - 18,34,14 )$
E) $( 37 , - 34 , - 27 )$

Quizplus · Accepted Answer

To find the cross product of two vectors, we can use the following formula:
$$\mathbf{u}	imes \mathbf{v} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \ u_1 & u_2 & u_3 \ v_1 & v_2 & v_3 \end{vmatrix}$$
where $\mathbf{i}, \mathbf{j},$ and $\mathbf{k}$ are the unit vectors in the $x,y,$ and $z$ directions, respectively. 
Plugging in the values from the question, we get:
$$\mathbf{u}	imes \mathbf{v} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \ 8 & 3 & 3 \ 2 & -1 & 5 \end{vmatrix}$$
Expanding along the first column, we get:
$$\mathbf{u}	imes \mathbf{v} = (3	imes 5 - 3 	imes (-1))\mathbf{i} - (8	imes 5 - 3 	imes 2)\mathbf{j} + (8	imes (-1) - 3	imes 2)\mathbf{k}$$
Simplifying, we get:
$$\mathbf{u}	imes \mathbf{v} = 18\mathbf{i} - 34\mathbf{j} - 14\mathbf{k}$$
Therefore, the answer is $\boxed{	extbf{(C)}\ (18, - 34, - 14)}.$

Given u=(8,3,3} and v={2,−1,5} find u×v\text { Given } \mathbf { u } = ( 8,3,3 \} \text { and } \mathbf { v } = \{ 2 , - 1,5 \} \text { find } \mathbf { u } \times \mathbf { v } Given u=(8,3,3} and v={2,−1,5} find u×v

$\text { Given } \mathbf { u } = ( 8,3,3 \} \text { and } \mathbf { v } = \{ 2 , - 1,5 \} \text { find } \mathbf { u } \times \mathbf { v }$