Unit vectors a and b are perpendicular and unit vector c is inclined at an angle

Question

Unit vectors \(\vec a\) and \(\vec b\) are perpendicular, and unit vector \(\vec c\) is inclined at an angle θ  to both \(\vec a \) and \(\vec b\) . If \(\vec c = \alpha \vec a + \beta \vec b + \gamma (\vec a \times \vec b)\) then

Answer 1

Since \(\vec a\) and \(\vec b\) and \(\vec c\) are unit vectors inclined at an angle θ we have

Similarly, by taking dot product on both sides of (i)