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If there is a line segment A.B on the plane with a length of 5, how many lines are there on the plane with distances of 2 and 3 from point AB?
Three, one vertical, two symmetrical
It is known that the angle between the line Mn and plane α is 45 ° and that the two points of Mn are on the same side of plane α and the distances to plane α are 5 and 2 respectively,
Finding the projective length of line segment Mn in plane α
5-2=3
tan45°=1
3*1=3
Given that the length of line AB is 10 and the distances from point a and B to plane α are 2 and 3 respectively, the angle between line AB and plane α is 0
Extend Ba so that it intersects plane α with point C, and then make a vertical line intersection plane α with D, e through point a and point B
If CDE is connected, ∠ BCE is the required value
Let AC = X
So sin ∠ BCE = ad / AC = be / BC
AD/AC=BE/BC =2/X=3/(10+X) X=4
sin∠BCE=AD/AC=2/4=1/2
∠BCE=30
If the line segment AB between two parallel planes α and β is 8, and the angle between AB and plane α is 45 degrees, then the distance between α and β is equal to
Distance x = abcos45 = 4 times root 5
The number of integer points whose distance from the number axis to the origin is less than 2 is x, the number of integer points whose distance is not more than 2 is y, and the number of integer points whose distance is equal to 2 is Z. find the value of X + y + Z
The integers whose distance from the number axis to the origin is less than 2 have - 1, 0, 1, so x = 3; the integers whose distance from the number axis to the origin is not more than 2 have - 2, - 1, 0, 1, 2, so y = 5; the integers whose distance from the number axis to the origin is equal to 2 have - 2, 2, so z = 2, - x + y + Z = 3 + 5 + 2 = 10
For example, the absolute value of - 3 is the distance between the point of - 3 and the origin__ The two numbers represented by a point with a distance of 3 to the origin are__ And__
For example, the absolute value of - 3 is the distance between the point of - 3 and the origin_ 3_ The two numbers represented by a point with a distance of 3 to the origin are_ 3_ And_ -3_
In the plane direct coordinate system xoy, point P is on the negative half axis of X axis, and the distance to the origin is 6, then the coordinate of point P is
The coordinates of point P are (- 6,0)
In the rectangular coordinate system as shown in the figure, there is an interface perpendicular to the coordinate plane. The interface is 45 ° to the X axis and passes through the coordinate origin O. there is a uniform electric field on the lower right side of the interface, the field strength is e, the direction is along the positive direction of the Y axis. There is a uniform magnetic field on the upper left side of the interface, the direction is perpendicular to the coordinate plane, and the size is unknown After a period of time, the particles return to the electric field area again from the coordinate origin o, regardless of the gravity of the particles? (2) What is the magnetic induction of the magnetic field? (3) The position coordinates of particles passing through the interface for the third time?
(1) The particle enters the magnetic field along the direction of the electric field and reaches the q-point on the interface. The coordinates of q-point are (B, b). According to the geometric knowledge, the displacement of particle from P to q is s = 2B. According to the kinetic energy theorem, 2qeb = 12mv2-0
As shown in the figure, in the plane rectangular coordinate system, point C (- 3,0), points a and B are respectively on the positive half axis of X axis and Y axis, and satisfy the root sign (o)
As shown in the figure, in the plane rectangular coordinate system, point C (- 3,0), points a and B are respectively on the positive half axis of X axis and Y axis, and satisfy the root sign (OB & # 178; - 3) + absolute value (oa-1) = 0
(1) Find the coordinates of point a and B
(2) If point P starts from point C and moves along ray CB at a speed of 1 unit per second, connect AP. Let the area of △ ABP be s and the movement time of point p be T seconds, find the functional relationship between S and T, and write out the value range of independent variable
(3) Under the condition of (2), is there a point P so that the triangle with points a, B and P as the vertex is similar to △ AOB? If so, please write the coordinates of point P directly; if not, please explain the reason
(1) Because √ (OB ^ - 3) + | oa-1 | = 0, there is ob = √ 3, OA = 1, because a and B are respectively on the positive half axis of X axis and Y axis, so there are a (1,0), B (0, √ 3)
(2) It can be found that BC = 2 √ 3, ab = 2, and AC = 1 + 3 = 4, it can be concluded that Δ ABC is a right triangle, ∠ ABC = 90 degrees
Point P starts from point C and moves along the ray CB at the speed of 1 unit per second. Through this condition, it can be concluded that CP = t and t ∈ [0,2 √ 3]
S = s Δ ABP = Pb * AB / 2 = (bc-pc) * 2 / 2 = 2 √ 3-T, where t ∈ [0,2 √ 3]
(3) If there is a point P that makes Δ ABP similar to Δ AOB, then from ∠ PBA = 90 degrees, Pb and ab are the two right angle sides of Δ ABP, and their proportion should meet the ratio of the two right angle sides in Δ AOB. Because OA and ob are the two right angle sides of Δ AOB, they are not equal to each other, ob / 0A = √ 3 / 1 = √ 3, so the ratio of the two right angle sides Pb and AB in Δ PAB should also be equal to √ 3, It's just that it's impossible to determine who is the best and who is the worst
If Pb is longer than AB, then Pb / AB = √ 3, then Pb = √ 3 * 2 = 2 √ 3, t = PC = bc-pb = 2 √ 3-2 √ 3 = 0. In this case, point P coincides with point C, and the coordinate of P is (- 3,0)
If AB is longer than Pb, then AB / Pb = √ 3, Pb = √ 3 * 2 / 3 = 2 √ 3 / 3, t = 2 √ 3-2 √ 3 / 3 = 4 √ 3 / 3, which satisfies the value range of T, so this point also exists
The linear equation passing through B (0, √ 3) and C (- 3,0) can be obtained as y = √ 3x / 3 + √ 3, and P is located on it, and YP = t / 2 = 2 √ 3 / 3 can be obtained from the geometric relationship, and XP = - 1 can be obtained by substituting it into the linear equation
So the P coordinate is (- 1,2 √ 3 / 3)
In the rectangular coordinate system xoy, the sum of distances from point m to point F1 (- radical 3,0) and F2 (radical 3,0) is 4. The locus C of point m intersects with the negative half axis of X axis at point a, but the straight line L: y = KX + B of a intersects with LOCUS C at different two points P and Q
1. Find the trajectory of C
2. When vector AP * vector AQ = 0, find the relationship between K and B, and prove that l is over a fixed point
1. According to the meaning of the topic, the trajectory of C is ellipse, C = radical 3,2a = 4, ｛ B = 1 ｛ C's trajectory equation is X & ｛ 178 / 4 + Y & ｛ 178; = 0; 2. According to the meaning of the topic, we can get the point a (- 2,0), let P (x1, Y1), q (X2, Y2), then the simultaneous equations get X & ｛ 178 / 4 + Y & ｛ 178; = 0; y = KX + B generation get (4K & ｛ 178; + 1) x & ｛ 178; + 8b
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