Take o as the coordinate origin, OE
The direction of is the positive direction of the X axis, and the spatial rectangular coordinate system O-XYZ as shown in the figure is established.
20 13 National Outline Volume Science Mathematics Page 10
Set |AB
| = 2, then A(2? ，0，0)，D(0，2？ ，0)，C(22，2？ ，0)，P(0，0，2)。 PC=(22，2？ ,2? )，PD
=(0,2? ,2? ).AP=(2，0，2)，AD
=(2,2? ,0).
Let the normal vector of planar PCD be n 1 = (x, y, z), then n 1? personal computer
=(x，y，z)？ (22,2? ,2? )=0,
n 1？ Parkinson's disease
=(x，y，z)？ (0,2? ,2? )=0,
You can get 2x-y-z = 0 and y+z = 0.
If y =- 1, X = 0 and Z = 1, then n 1=(0 = (0,-1, 1).
Let the normal vector of the planar PAD be n2 = (m, p, q), then n2? AP=(m，p，q)？ (2，0，2)=0，n2？ advertisement
=(m，p，q)？ (2,2? 0) = 0, we can get m+q = 0 and m-p = 0.
Take m = 1 to get p = 1 and q =- 1, so N2 = (1, 1). So COS < N 1, N2 > =
12 126
||||3
nnnn。
Since < N 1, N2 > is equal to the plane angle of dihedral angle A-PD-C, the size of dihedral angle A-PD-C is 6πarccos3.
. 20.
Solution: (1) Note that A 1 means the event "the result of the second game is victory".
A2 means the event "A entered in the third game and the result was negative", and A means the event "A was the referee in the fourth game". So a = A 1? A2。
P(A)=P(A 1？ A2)= P(a 1)P(A2)= 1
14
. (2) The possible values of x are 0, 1, 2.
Note A3 stands for the third game, B wins C, B 1 stands for the first game, B wins C, B2 stands for the second game, B wins A, B3 stands for the third game, and B loses.
Then p (x = 0) = p (b 1? B2？ A3)=P(B 1)P(B2)？ P(A3)= 18，P(X=2)=P( 1B？ B3)=P( 1B)P(B3)= 1
four
，P(X = 1)= 1-P(X = 0)-P(X = 2)= 1 15 1848？ ，EX=0？ P(X=0)+ 1？ P(X= 1)+2？ P(X=2)=9
eight
.
2 1.
(1) Solution: Know ca from the problem.
= 3, that is, 222aba? = 9, so B2 = 8a2.
.
So the equation of c is 8x2.
-y2
=8a2
Substitute y = 2 into the above formula to get 2.
1
2
xa？ Judging from the topic, 2
1
262
Answer?
The solution is A2 = 1. So A = 1 and B = 22.
(2) Prove that the equation of f 1 (-3,0 (-3,0), F2 (3,0) and c is 8x2 from (1).
-y2
=8.①
The equation of l can be set as y = k (x-3), < 22k, substituted into ①, and simplified as (k2.
-8)x2
-6k2
x+9k2
+8=0.
Let A(x 1, y 1) and B(x2, y2), then x 1 ≤- 1, x2≥ 1, x1+x.