Question

Find the cross product of v = (2, -1, 3) and w=(1, 0, -5).

Answer 1

Step-by-step explanation:

The vectors are

v = (2, -1, 3)

w= (1, 0, -5).

v x w =

`\begin{gathered} \begin{bmatrix}{i} & {j} & {k} \\ {2} & {-1} & {3} \\ {1} & {0} & {-5}\end{bmatrix} \\ i((-1*-5)-(3*0))-j((2*-5)\text{ -\lparen3}*1))+k((2*0)-(-1*1) \\ =\text{ i\lparen5-0\rparen - j\lparen-10-3\rparen+k\lparen0+1\rparen} \\ =\text{ \textbraceleft5; 13; 1\textbraceright} \end{gathered}`

The cross product is

{5, 13, 1}