Magnitude of A+B

Correct Answer

B — 7

Concept and Reasoning

Adding components gives A+B=(1+5)a_x+2a_y+(3−6)a_z=6a_x+2a_y−3a_z. Its magnitude is √(6²+2²+3²)=√49=7, which corresponds to option B.

Calculation / Key Relation

|A+B|=√(6²+2²+(−3)²)=7

Exam Takeaway

Add vector components first, then take the Euclidean magnitude.

Common Mistake

Do not add vector magnitudes directly unless the vectors are collinear in the same direction.