Mathematics — Analysis And Approaches

Mathematics — Analysis and Approaches

Problem

Let

\vec{v} = a\vec{i} + b\vec{j} + c\vec{k}

be the vector representing the space diagonal of a prism, where

a

b

c

are positive real numbers. If the angle between this vector and the plane spanned by

\vec{i}

and

\vec{j}

30^{\circ}

, express

c

in terms of

a

and

b