Previous Year Question
Given vectors A = ax + 3az and B = 5ax + 2ay – 6az, the value of |A + B| will be
Correct answer: B
Explanation
Adding components gives A+B=(1+5)ax+2a_y+(3−6)az=6a_x+2a_y−3a_z. Its magnitude is √(6²+2²+3²)=√49=7, which corresponds to option B.
Formula
|A+B|=√(6²+2²+(−3)²)=7
Step-by-step solution
Correct Answer
B — 7
Concept and Reasoning
Adding components gives A+B=(1+5)ax+2a_y+(3−6)az=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.
Common mistake
Do not add vector magnitudes directly unless the vectors are collinear in the same direction.
Exam tip
Add vector components first, then take the Euclidean magnitude.
Quick method
Add vector components first, then take the Euclidean magnitude.