MHB Did my book do this wrong? (Vector Cross Product)

[Pindrought]

Reading a book about 3d math, and I am confused as to what happened on this Vector Cross Product problem. I'm thinking there was just an error that wasn't caught.

For the first row, instead of (3)(8)-(-4)(-5) shouldn't it have been (3)(8)-(4)(-5) and had the same displayed result of 44?
And for the second row, instead of (-4)(2)-(1)(8) shouldn't it have been (4)(2)-(1)(8) and had the result of 0?
For the last row, shouldn't the final result be -11?

Thanks!

 

[Deveno]

The book is indeed wrong:

$(1,3,4) \times (2,-5,8) = ((3)(8) - (4)(-5), (4)(2) - (1)(8), (1)(-5) - (3)(2))$

$= (44,0,-11)$ which speaks somewhat ill of the original author and proof-reader of your text.

 

[Opalg]

Reading a book about 3d math, and I am confused as to what happened on this Vector Cross Product problem. I'm thinking there was just an error that wasn't caught.

For the first row, instead of (3)(8)-(-4)(-5) shouldn't it have been (3)(8)-(4)(-5) and had the same displayed result of 4?
And for the second row, instead of (-4)(2)-(1)(8) shouldn't it have been (4)(2)-(1)(8) and had the result of 0?
For the last row, shouldn't the final result be -11?

Thanks!

There are at least two misprints/errors in the example. It looks as though the author intended to write $$\begin{bmatrix}1\\3\\ {\color{red}-}4 \end{bmatrix} \times \begin{bmatrix}2\\-5\\ 8 \end{bmatrix} = \begin{bmatrix}(3)(8) - (-4)(-5)\\(-4)(2) - (1)(8)\\ (1)(-5) - (3)(2) \end{bmatrix} = \begin{bmatrix}4\\-16\\ {\color{red}-11} \end{bmatrix}.$$

 

[Pindrought]

Thank you very much!