- #1

CaliforniaRoll88

- 35

- 6

- 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.

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

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.

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