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The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors ⃗a, ⃗b and ⃗c respectively. Then, choose the correct relation for these vectors.

Asked in JEE Main 26th Feb 2nd Shift 2021 · Scalar product and projections

• (1) ⃗b = 2⃗a + ⃗c
• (2) ⃗b = ⃗a - ⃗c
• (3) ⃗b = ⃗a - 2(⃗a·⃗c)⃗c
• (4) ⃗b = ⃗a + 2⃗c

Step-by-step solution

Why the other options are wrong

• (1) Adds the normal instead of reversing the normal component; the result is not even a unit vector.
• (2) Subtracts the whole normal instead of twice the normal component of ⃗a.
• (4) Adds twice the normal; the tangential part is right but the normal part is not reversed.

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