question_answer

The incident ray on a surface is along the unit vector \[\hat{v},\]the reflected ray is along the unit vector \[\hat{w}\]and the normal is along unit vector \[\hat{a}\] outwards. Express \[\hat{w}\]in terms of \[\hat{a}\]and \[\hat{v}\].

A)  \[\hat{w}=\hat{v}-2(\hat{a}.\hat{v})\,\hat{a}\] 

B)  \[\hat{w}=\hat{v}-3(\hat{a}.\hat{v})\,\hat{a}\]

C)  \[\hat{w}=\hat{v}-4(\hat{a}.\hat{v})\,\hat{a}\] 

D)  \[\hat{w}=\hat{v}+2(\hat{a}.\hat{v})\,\hat{a}\]

E)  None of these