A vector a = α î + 2ĵ + β k̂ lies in the plane determined by b = î + ĵ and c = ĵ + k̂, and it bisects the angle between b and c. Which of the following can be the values of α and β?

Question

Accepted Answer

α = 1, β = 1. Since |b|=|c|=sqrt2, the internal bisector is along b+c=(1,2,1). For a=(alpha,2,beta) to be parallel to (1,2,1) with middle component 2, take the vector (1,2,1) itself, giving alpha=1, beta=1.

A vector a = α î + 2ĵ + β k̂ lies in the plane determined by b = î + ĵ and c = ĵ + k̂, and it bisects the angle between b and c. Which of the following can be the values of α and β?

Solution

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