The solution to a math problem in the national college entrance examination volume I

I won't talk about the steps of establishing the coordinate system. AD is the x axis, DC is the y axis, and SD is the z axis.

1, let E(a, b, c)

Then the vectors SC = (0,2, -2) and SB = (1, 1, 2) can easily find the SBC normal vector N 1 = (1, 1).

Get DC = (0,2,0), Germany =(a, b, c), and the normal vector N2 of EDC = (c, 0, -a).

N 1*n2=c-a=0, so A = C.

And e is on SB, so a/ 1=b/ 1=2-c/ 2, and the solution is a=b=2/3, so SE=2EB.

2. In the first question, we can know that the normal vector of EDC is (2/3,0, -2/3). Note that the z-axis coordinate is negative.

At the same time, we can find that the normal vector of ADE is (0, 1,-1). Pay attention to taking the z-axis coordinate as negative.

The dihedral angle formula shows that the cosine of the included angle is 1/2 and the included angle is π/3.