JEE Advance - Mathematics (2005 - No. 2)
If the incident ray on a surface is along the unit vector $$\widehat v\,\,,$$ the reflected ray is along the unit vector $$\widehat w\,\,$$ and the normal is along unit vector $$\widehat a\,\,$$ outwards. Express $$\widehat w\,\,$$ in terms of $$\widehat a\,\,$$ and $$\widehat v\,\,.$$


$$\widehat w = \widehat v + 2(\widehat a \cdot \widehat v)\widehat a$$
$$\widehat w = -\widehat v + 2(\widehat a \cdot \widehat v)\widehat a$$
$$\widehat w = \widehat v - 2(\widehat a \cdot \widehat v)\widehat a$$
$$\widehat w = \widehat a - 2(\widehat v \cdot \widehat a)\widehat v$$
$$\widehat w = \widehat v - (\widehat a \cdot \widehat v)\widehat a$$
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