Question

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

Answer 1

Answer:

Explanation:

The vectors are

v = (2, -1, 3)

w= (1, 0, -5).

v x w =

$\begin{gathered} \begin{bmatrix}{i} & {j} & {k} \\ {2} & {-1} & {3} \\ {1} & {0} & {-5}\end{bmatrix} \\ i((-1\times-5)-(3\times0))-j((2\times-5)\text{ -\lparen3}\times1))+k((2\times0)-(-1\times1) \\ =\text{ i\lparen5-0\rparen - j\lparen-10-3\rparen+k\lparen0+1\rparen} \\ =\text{ \textbraceleft5; 13; 1\textbraceright} \end{gathered}$

The cross product is

{5, 13, 1}