Chapter 9, Problem 109RE

To determine

To calculate:The cross product of vectors $v\times u$ where cross product of $u\times v=2i-3j+k$ .

Answer to Problem 109RE

The cross product of vectors $v\times u=\left(-2i+3j-k\right)$ .

Explanation of Solution

Given information:

The cross product of vectors are given as:

  $u\times v=2i-3j+k$

Formula used:

let $u$ and $v$ are two vectors,

then, algebraic property of the cross product is $u\times v=-\left(v\times u\right)$

Calculation:

Consider the cross product of vectors,

  $u\times v=2i-3j+k$

Apply the algebraic property of the cross product,

  $\begin{array}{c}u\times v=-\left(v\times u\right)\\ 2i-3j+k=-\left(v\times u\right)\end{array}$

Multiply by the $-$ on the both sides of equation,

  $\begin{array}{c}\left(v\times u\right)=-\left(2i-3j+k\right)\\ =\left(-2i+3j-k\right)\end{array}$

Thus, the cross product of vectors is $v\times u=\left(-2i+3j-k\right)$