Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a = 2î + 3ĵ − k̂ and b = î − 2ĵ + k̂. A. (15î + 5ĵ)/√10 B. 15î + 5ĵ C. (3î + ĵ)/√10 D. 5(3î + ĵ) Answer: A) (15î + 5ĵ)/√10 Explanation: Resultant R = a + b = 3î + ĵ + 0k̂. Magnitude |R| = √(9 + 1) = √10. Unit vector = (3î + ĵ)/√10. Vector of magnitude 5 = 5 × (3î + ĵ)/√10 = (15î + 5ĵ)/√10.

imo class 12 vector algebra

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a = 2î + 3ĵ − k̂ and b = î − 2ĵ + k̂.

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Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a = 2î + 3ĵ − k̂ and b = î − 2ĵ + k̂.

A. (15î + 5ĵ)/√10
B. 15î + 5ĵ
C. (3î + ĵ)/√10
D. 5(3î + ĵ)

Answer: A) (15î + 5ĵ)/√10

Explanation: Resultant R = a + b = 3î + ĵ + 0k̂. Magnitude |R| = √(9 + 1) = √10. Unit vector = (3î + ĵ)/√10. Vector of magnitude 5 = 5 × (3î + ĵ)/√10 = (15î + 5ĵ)/√10.

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