Does the book have an error in the addition of these two vectors?

[CaliforniaRoll88]

Homework Statement

Given the vectors $\vec M = -10\hat a_x+4\hat a_y-8\hat a_z$ and $\vec N = 8\hat a_x+7\hat a_y-2\hat a_z$ , find: (a) a unit vector in the direction of $-\vec M - 2\vec N$

Relevant Equations

$\hat a_B=\frac {\vec B} {\sqrt {B^2_x+B^2_y +B^2_z}}$

(a)
$$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$
Unit Vector Formula
$$\hat a_A=\frac{26\hat a_x+10\hat a_y+4\hat a_z}{\sqrt {26^2+10^2+4^2}}$$
$$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$
The book gives $0.92\hat a_x+0.36\hat a_y+0.4\hat a_z$
Not sure how the book get 0.4 for the z-component. Maybe it's an error.

 

[DrClaude]

Homework Statement: Given the vectors $\vec M = -10\hat a_x+4\hat a_y-8\hat a_z$ and $\vec N = 8\hat a_x+7\hat a_y-2\hat a_z$ , find: (a) a unit vector in the direction of $-\vec M - 2\vec N$

$$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$

I assume that the latter is correct (plus sign, not minus, in front of $2N$).

$$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$
The book gives $0.92\hat a_x+0.36\hat a_y+0.4\hat a_z$
Not sure how the book get 0.4 for the z-component. Maybe it's an error.

Considering that the answer is given with two significant figures and that $0.4$ only has one, this looks like a typo (missing 1).

 

[CaliforniaRoll88]

Much appreciated.