An auto-rickshaw travels along a path given by the vector 3î + 4ĵ. The magnitude of its acceleration is 10 m/s² directed parallel to its path. The acceleration vector is: A. 6î + 8ĵ B. 30î + 40ĵ C. 10î + 10ĵ D. 10(3î + 4ĵ) Answer: A) 6î + 8ĵ Explanation: Unit vector along path = (3î + 4ĵ)/√(3²+4²) = (3î + 4ĵ)/5. Acceleration vector = Magnitude × Unit vector = 10 × (3î + 4ĵ)/5 = 2(3î + 4ĵ) = 6î + 8ĵ.

imo class 12 vector algebra

An auto-rickshaw travels along a path given by the vector 3î + 4ĵ. The magnitude of its acceleration is 10 m/s² directed parallel to its path. The acceleration vector is:

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An auto-rickshaw travels along a path given by the vector 3î + 4ĵ. The magnitude of its acceleration is 10 m/s² directed parallel to its path. The acceleration vector is:

A. 6î + 8ĵ
B. 30î + 40ĵ
C. 10î + 10ĵ
D. 10(3î + 4ĵ)

Answer: A) 6î + 8ĵ

Explanation: Unit vector along path = (3î + 4ĵ)/√(3²+4²) = (3î + 4ĵ)/5. Acceleration vector = Magnitude × Unit vector = 10 × (3î + 4ĵ)/5 = 2(3î + 4ĵ) = 6î + 8ĵ.

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