The vector \( a =α i +2 j +β k \) lies in the plane of the vector \( b = i + j \) and \( c = j + k \) and bisects the angle between \( b \) and \( c \) . Then, which one of the following gives possible...

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Question 43

Mathematics Scalar and Vector Products Hard

The vector \(\vec{a}=α \hat{i}+2\hat{j}+β \hat{k}\) lies in the plane of the vector \(\vec{b}=\hat{i} + \hat{j}\) and \(\vec{c}=\hat{j} + \hat{k}\) and bisects the angle between \(\vec{b}\) and \(\vec{c}\). Then, which one of the following gives possible values of α and β ?

(A) α = 2, β = 2

(B) α = 1, β = 2

(C) α = 2, β = 1

(D) α = 1, β = 1

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Correct Solution: Option D

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