Скачать или смотреть Let â be a unit vector perpendicular to the vectors b = î-2ĵ+3k̂ and c = 2î+3ĵ-k̂, and | JEE MAIN

Let â be a unit vector perpendicular to the vectors →b = î-2ĵ+3k̂ and →c = 2î+3ĵ-k̂, and makes an angle of cos⁻¹(-1/3) with the vector î+ĵ+k̂. If â makes an angle of π/3 with the vector î+αĵ+k̂, then the value of α is: (1) -√3 (2) √6 (3) -√6 (4) √3.

In this video, I tackle an advanced 3D vector problem involving unit vectors and multiple geometric constraints. We need to find a unit vector â that is perpendicular to both vectors →b = î-2ĵ+3k̂ and →c = 2î+3ĵ-k̂, makes an angle of cos⁻¹(-1/3) with î+ĵ+k̂, and an angle of π/3 with î+αĵ+k̂. Watch as I systematically solve for the value of α using vector algebra, dot product properties, and cross product techniques. I'll demonstrate how to handle multiple vector constraints simultaneously, calculate a unit normal vector to a plane, and apply the angle formula between vectors. This problem combines multiple vector concepts that are crucial for competitive exams and tests your understanding of 3D geometry at an advanced level.

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