In the triangular pyramid p-abc, PA is perpendicular to the plane ABC, ∠ BAC = 60 °, PA = AB = AC = 2, and E is the midpoint of PC The cosine of the angle between AE and Pb and the volume of a-ebc are calculated

In the triangular pyramid p-abc, PA is perpendicular to the plane ABC, ∠ BAC = 60 °, PA = AB = AC = 2, and E is the midpoint of PC The cosine of the angle between AE and Pb and the volume of a-ebc are calculated

1. ∵ AB = AC, ∠ BAC = 60 °∵ ABC equilateral ∵ BC = AB = 2 is the midpoint of BC, where EF and AF ∵ e are the midpoint of PC, f is the midpoint of BC, EF is the median line of △ PBC, EF ∥ Pb ∵ AEF is the angle between AE and Pb, let α∵ PAC be the isosceles right triangle, AE = √ 2PB = 2 √ 2ef = Pb / 2 = √ 2AF = √ 3cos α = (AE