If the scalar product of the vector a with the vectors 3î − 5k̂, 2î + 7ĵ and î + ĵ + k̂ are respectively −1, 6 and 5, find the vector a. A. 3î + 2k̂ B. 3î + ĵ − k̂ C. î + 2ĵ + 2k̂ D. 3î + k̂ Answer: A) 3î + 2k̂ Explanation: Let a = xî + yĵ + zk̂. Then 3x − 5z = −1, 2x + 7y = 6 and x + y + z = 5. Solving gives x = 3, y = 0, z = 2, so a = 3î + 2k̂.

imo class 12 vector algebra

If the scalar product of the vector a with the vectors 3î − 5k̂, 2î + 7ĵ and î + ĵ + k̂ are respectively −1, 6 and 5, find the vector a.

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If the scalar product of the vector a with the vectors 3î − 5k̂, 2î + 7ĵ and î + ĵ + k̂ are respectively −1, 6 and 5, find the vector a.

Answer: A) 3î + 2k̂

Explanation: Let a = xî + yĵ + zk̂. Then 3x − 5z = −1, 2x + 7y = 6 and x + y + z = 5. Solving gives x = 3, y = 0, z = 2, so a = 3î + 2k̂.