how to dot product two vectors with different planes?
I have vectors $A$,$B$ and $C$, vectors $A$ and $B$ is on $xy$ plane while vector $C$ is on $xz$ plane. I need to find the dot product of $A.C$ how should I do that? my book says that dot product of two vectors can be expressed in terms of their rectangular components. vector $B$ lies in $y$-axis. vector $A$ makes $60$ degrees to $B$, vector $C$ makes $37$ degrees to $x$-axis. $A=10$, $B=8$ and $C=5$.
please help me to solve this problem
B lies in y- axis , then A makes 30 degrees with x-axis, so that:
$$A=10\cos30\, i+10\sin30\,j\qquad A=5\sqrt3\,i+5\,j$$
$$C=5\cos37\,i+5\sin37\,k\quad =4\,i+3\,k$$
$$A.C=20\sqrt3$$