Question

If a vector A = ax + 2a y + 3az , find its magnitude and direction

Answer 1

$A=a\hat{x}+2a\hat{y}+3a\hat{z}$

$$|A|=\sqrt{a^2+(2a)^2+(3a)^2}=\sqrt{14a^2}\\|A|=\sqrt{14}a$$

$\hat{n}=\frac{A}{|A|}$

$\hat{n}=\frac{a\hat{x}+2a\hat{y}+3a\hat{z}}{\sqrt{14}a}$

$\hat{n}=\frac{\hat{x}+2\hat{y}+3\hat{z}}{\sqrt{14}}$