Unit Vector

If the incident ray on a surface is along the unit vector vec v , the reflected ray is along the unit vector vec w and the normal is along the unit vector vec a outwards, express vec w in terms of vec a and vec v

If the incident ray on a surface is along the unit vector vec v , the reflected ray is along the unit vector vec w and the normal is along the unit vector vec a outwards, express vec w in terms of vec a and vec v

If P(-1,2) and Q(3,-7) are two points, express the vectors vec(PQ) in terms of unit vectors hatiand hatj . Also find the distance between points P and Q. What is the unit vector in the direction of vec(PQ) ? Verify that magnitude of unit vector indeed unity.

(a) Derive an expression for unit vector along reflected ray (hat r) if unit vectors hat i and hat n represents unit vectors along incident light ray and normal (at point of reflection and outward from surface) respectively. (b) If vector along the incident ray on a mirror is -2 hat i+ 3 hat j + 4 hat k . Considering the x-axis to be along the normal. Then, find the unit vector along the reflected ray.