Directional cosine

Let $\boldsymbol{A} \neq {\bf0}$ and let the angle between the direction of $\boldsymbol{A}$ and $x$-axis，$y$-axis，$z$-axis is $\alpha,\beta,\gamma$ respectively. Then we say

$$\cos{\alpha},\ \cos{\beta},\ \cos{\gamma}$$

is the directional cosine of $\boldsymbol{A}$.

For $\boldsymbol{A} = A_{1}\:\boldsymbol{i} + A_{2}\:\boldsymbol{j} + A_{3}\:\boldsymbol{k}$，we can express

$$\boldsymbol{A} = \vert\boldsymbol{A}\vert(\cos{\alpha}\:\boldsymbol{i} + \cos{\beta}\:\boldsymbol{j} + \cos{\gamma}\:\boldsymbol{k})$$

Question 1..7  

The position vector of point A forms an angle between the $x$ axis with $\ pi/4$, the $y$ axis with $\pi/3$, and the $z$ axis with $\pi/6$, and its magnitude is 6. Find the coordinates of A．