$\"\"$

The direction angles of the vector are $\"\"$ and $\"\"$ .

Use direction cosines, since we have known two direction angles and we have to find the third

one use the following equation.

$\"\"$ .

Where $\"\"$ and $\"\"$ .

Substiute the values in the equation $\"\"$ .

$\"\"$

Therefore, the third vector is $\"\"$ .

$\"\"$

The third unknown vector is $\"\"$ .