If the distance between the two ends of line AB and plane α is equal to 1, then the position relationship between line AB and plane α is?

Parallel, intersect

As shown in the figure, the straight line AC ‖ BD connects ab. the straight line AC, BD and the line AB divide the plane into four parts: ①, ②, ③ and ④. It is stipulated that each point on the line does not belong to any part. When the moving point P falls on a certain part, it connects PA and Pb to form three angles ∠ PAC, ∠ APB and ∠ PBD. (hint: the angle formed by two overlapping rays with common end point is 0 ° angle)
(1) When the moving point P falls in the first part, it is proved that: ∠ APB = ∠ PAC + ∠ PBD; (2) when the moving point P falls in the second part, is ∠ APB = ∠ PAC + ∠ PBD Tenable? (whether the direct answer is true or not) (3) when the moving point P falls in the third part, comprehensively explore the relationship among ∠ PAC, ∠ APB, ∠ PBD, and write the specific location of the moving point P and the corresponding conclusion. Choose one of the conclusions to prove

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In the rectangular coordinate system xoy, the starting edge of angle a is the non negative half axis of X axis, and the ending edge is the ray L: y = (2 radical sign 2) x, (x > = 0) (1) find the value of sin (a + 30 °)
(2) If the vertex P.Q is the moving point at the beginning and end of angle α, and PQ = 4, the coordinates of P and Q are obtained when the area of triangle poq is the largest

1
Ray L: y = 2 √ 2x (x > = 0)
tana=2√2 cosa>0,sina>0
(cosa)^2=1/(1+(tana)^2)=1/9
cosa=1/3 sina=2√2/3
sin(a+30)=sinacos30+cosa*sin30=(2√2/3)(√3/2)+(1/3)*(1/2)=(1+2√6)/6
two
p(x0,0),q(x1,2√2x1)
pq^2=(x0-x1)^2+(2√2x1)^2=x0^2+9x1^2-2x0x1=16
Spoq=x0 *(2√2x1)/2=x0*(√2x1)

In the rectangular coordinate system, points a and B are on the positive half axis of X axis, the circle C with ab as the chord is tangent to point E on Y axis, the coordinate of point E is (0,2), and the length of AE is the root sign
In the rectangular coordinate system, the points a and B are on the positive half axis of the x-axis, the circle C with ab as the chord is tangent to the point E on the y-axis, the coordinate of point E is (0,2), and the length of AE is the root sign. 5

Connect AE, AC and make CD vertical ab
In AEO
E (2,0) AE = root 5,
OA=1,A（1,0).
Let ⊙ C radius be r
In ADC
CD=OE=2 AD=OD-OA=r-OA=r-1
AC^2=AD^2+DC^2
r^2=(r-1)^2+2^2
r=2.5
OB=（2.5-1）*2+1=4
B（4,0）

As shown in the figure, put RT △ ABC in the rectangular coordinate system, where ∠ cab = 90 ° BC = 5,
The coordinates of points a and B are (1,0), (4,0) respectively. Translate △ ABC to the right along the X axis. When point C falls on the curve y = 24 / x, the area swept by segment BC is ()

As shown in the figure, place RT △ ABC in the rectangular coordinate system, where ∠ cab = 90 °, BC = 5, the coordinates of points a and B are (1,0), (4,0), respectively. Translate △ ABC to the right along the X axis. When point C falls on the curve y = 24 / x, the area swept by line BC is (8)

As shown in the figure, place RT △ ABC in the rectangular coordinate system, where ∠ cab = 90 °, BC = 5, and the coordinates of points a and B are (1,0), (4,0) respectively. Translate △ ABC to the right along the X axis. When point C falls on the straight line y = 2x-6, the swept area of line BC is ()
A. 4B. 8C. 16D. 82

The coordinates of point a and B are (1,0), (4,0), ab = 3, BC = 5, ∵ ∠ cab = 90 °, AC = 4, and the coordinates of point C are (1,4). When point C falls on the line y = 2x-6, let y = 4, and get 4 = 2x-6. The solution is x = 5, the translation distance is 5-1 = 4, and the swept area of line BC is 4 × 4 = 16

Place RT △ ABC in the rectangular coordinate system, where ∠ cab = 90 ° and BC = 5, the coordinates of points a and B are (1,0) and (4,0) respectively, and set △ ABC to the right along the x-axis
Translate △ ABC to the right along the x-axis. When point C falls on the line y = 2x-6, calculate the area swept by line BC

First of all, the coordinate of C is (0,4). When △ ABC moves to the right along the X axis, the y value of the coordinate of C does not change to 4, so 4 = 2x-6,
Get: x = 5, the area swept by BC is: S = XC * YC. Get s = 20

In the angular coordinate system, the coordinates of vertex a of RT △ ABC are (- 1,5), the coordinates of vertex B are (9,5), and point C is on the x-axis

There are three cases of point C, C (9,0) or C (- 1,0) or C (4,0). You can draw a picture to verify it

As shown in the figure, there is an isosceles triangle OAB in the rectangular coordinate system, O is the origin, the coordinates of vertex a are (33,3), and the coordinates of B are (6,0). (1) make a figure △ OAB ′ B ′ symmetrical about the y-axis in the coordinate system; (2) rotate △ OAB 90 ° clockwise around point O to get △ OCD. Draw △ OCD, and write out the coordinates of point C; (3) guess the degree of ∠ AOB, and explain the reason ．

(1) Figure △ OA ′ B ′ is correct (2 points) (2) draw △ OCD is correct (4 points); point C (3, - 33) (5 points) (3) guess the degree of ∠ AOB is 30 ° (6 points) reason: make AE ⊥ X axis in e through a, take the midpoint of Ao as F, connect EF, then in RT △ AEO, ∫ isosceles triangle OAB, OB = OA = 6, ∧ oblique

In Cartesian coordinate system, point O is the coordinate origin, a (2, - 4), and moving point B is on the coordinate axis?

4
If the triangle ABC is isosceles triangle and OA = ob is satisfied, then the trajectory of point B is in the circle with o as the center and passing through point a
Because point B is on the coordinate axis and there are four intersections between the circle and the coordinate axis, there are four points B satisfying the condition

If the distance between the two ends of line AB and plane α is equal to 1, then the position relationship between line AB and plane α is?