Question

L0. A triangle has verticen at A(2,3, 1), B(-1, 1, 2), C(1, -2, 3). Find the acute angle which the median to side AC makes with aide BC. Ana.

Answer 1

Let BM is the median to side AC, M(1.5, 0.5, 2).

$\vec{BM}=(2.5,~-0.5,~0),$

$\vec{BC}=(2,~-3,~1).$

$\vec{BM}\cdot \vec{BC}=6.5,$

$|\vec{BM}|=\sqrt{6.5},$

$|\vec{BC}|=\sqrt{14},$

$\alpha=arccos\frac{\vec{BM}\cdot \vec{BC}}{|\vec{BM}|\cdot|\vec{BC}|}=47°.$