important vector doubts

And what is \vec{a} ?

2. Let X,Y and Z be unit vectors such that X+Y+Z = a, Xx(YxZ)=b,
(X x Y) x Z =c.
a.X= 3/2 , a.Y=7/4 and |a|=2. Find X , Y, and Z in terms of a, b and c.

see wat i did i assumed \vec{a} to be along the x axis and \vec{c} along the y axis...now \vec{b} will make 30° angle with the x axis..
tan30° = \vec{c} / \vec{a} = 1/√3

so (\vec{c} + √3\vec{a})/2 = \vec{b}

so from here u will get \vec{c} = 2 \vec{b} - √3\vec{a}