Let and are vertices of a triangle and its median through is equally inclined to the…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let

A(2\hat{i} + 3\hat{j} + 5\hat{k}), B(-\hat{i} + 3\hat{j} + 2\hat{k})

and

C(\lambda\hat{i} + 5\hat{j} + \mu\hat{k})

are vertices of a triangle and its median through

A

is equally inclined to the positive directions of the axes. The value of

2\lambda - \mu

is equal to