As shown in the figure, in the cuboid abcd-a1b1c1d1, ab = ad = 1, Aa1 = 2, M is the midpoint of edge CC1. (II) prove that plane ABM is perpendicular to plane A1B1

As shown in the figure, in the cuboid abcd-a1b1c1d1, ab = ad = 1, Aa1 = 2, M is the midpoint of edge CC1. (II) prove that plane ABM is perpendicular to plane A1B1

Because c1d1 ‖ B1a1, so ∠ ma1b1 is the angle formed by the out of plane straight line a1m and c1d1, because A1B1 ⊥ plane bcc1b1, so ∠ a1b1m = 90 ° and A1B1 = 1, b1m = radical 2, so tan ∠ ma1b1 = radical 2, that is, the tangent value of the angle formed by the out of plane straight line a1m and c1d1 is radical 2. (2) prove that by A1B1 ⊥ plane bcc1b1