Directional cosine

Let $\boldsymbol{A} \neq {\bf0}$ and let the angle between the direction of $\boldsymbol{A}$ and $x$

-axis，

-axis，

-axis is $\alpha,\beta,\gamma$ respectively. Then we say

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

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

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

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．