Find a vector whose magnitude is 3 units and which is perpendicular to each of the vectors a = 3î + ĵ − 4k̂ and b = 6î + 5ĵ − 2k̂. A. (2î − 2ĵ + k̂) B. −(2î − 2ĵ + k̂) C. ±(2î − 2ĵ + k̂) D. ±(î − ĵ + k̂) Answer: C) ±(2î − 2ĵ + k̂) Explanation: a × b = î(−2 + 20) − ĵ(−6 + 24) + k̂(15 − 6) = 18î − 18ĵ + 9k̂. Magnitude = √(324 + 324 + 81) = √729 = 27. Unit vector = (18î − 18ĵ + 9k̂)/27 = (2î − 2ĵ + k̂)/3. Vector of magnitude 3 = ±3 × (2î − 2ĵ + k̂)/3 = ±(2î − 2ĵ + k̂).

imo class 12 vector algebra

Find a vector whose magnitude is 3 units and which is perpendicular to each of the vectors a = 3î + ĵ − 4k̂ and b = 6î + 5ĵ − 2k̂.

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Find a vector whose magnitude is 3 units and which is perpendicular to each of the vectors a = 3î + ĵ − 4k̂ and b = 6î + 5ĵ − 2k̂.

A. (2î − 2ĵ + k̂)
B. −(2î − 2ĵ + k̂)
C. ±(2î − 2ĵ + k̂)
D. ±(î − ĵ + k̂)

Answer: C) ±(2î − 2ĵ + k̂)

Explanation: a × b = î(−2 + 20) − ĵ(−6 + 24) + k̂(15 − 6) = 18î − 18ĵ + 9k̂. Magnitude = √(324 + 324 + 81) = √729 = 27. Unit vector = (18î − 18ĵ + 9k̂)/27 = (2î − 2ĵ + k̂)/3. Vector of magnitude 3 = ±3 × (2î − 2ĵ + k̂)/3 = ±(2î − 2ĵ + k̂).

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