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In mathematical geometry, there are two points a and B on the edge of a dihedral angle of 120 degrees. AC and BD are the dihedral angles respectively There are two points a and B on the edge of the dihedral angle of 120 degrees. AC and BD are the line segments perpendicular to AB in the two planes of the dihedral angle. Given AB = 4, AC = 6 and BD = 8, we can find the length of CD
Make parallel line ad 'of BD and connect DD'
AD'=BD=8 DD'=AB=4 CD'⊥DD'
CD'^2=AC^2+AD'^2-2*AC*AD'*cos120°=36+64+48=148
CD^2=CD'^2+DD'^2=148+16=164
CD=√164=2√41
The angle between AB and plane α is 30 °, the angle between AC and plane α is 60 °, ab = 6, AC = 8, diagonal AB.AC The projective ab '. AC' in α and ab '⊥ AC', find BC
Let B be BD ⊥ CC 'in D. ab' = abcos30 = 3, radical 3, AC '= accos60 = 4, ab' ⊥ AC ', so B' C '= radical 43. BB' = absin30 = 3, CC '= acsin60 = 4, radical 3, so DC = 4, radical 3-3. In triangle DCB, according to Pythagorean theorem, BC ^ 2 = DC ^ 2 + BD ^ 2 = DC ^ 2 + B' C '^ 2 = 100-24, radical 3
The distance from point a to a is 1, passing through point a leads to an oblique line of plane a, and intersects plane a at point B. If AB = 2, find the angle between line AB and plane a
Through the current a as AC ⊥ plane a at point C, connect BC;
Then ∠ ABC is the angle between line AB and plane a, and AC is the distance from point a to a, that is, AC = 1;
Because, AC ⊥ plane a, BC ∈ plane a,
So, AC ⊥ BC;
In RT △ ABC, ∠ ACB = 90 °, ab = 2 = 2Ac,
It can be concluded that the angle between line AB and plane a is ∠ ABC = 30 °
Let the distance from a to plane α be a. from point a, make two oblique line segments AB and AC of plane α at 45 and 30 degrees angles with plane α respectively, and the angle BAC = 90 degrees
What is the distance between the two oblique feet B and C?
Let ad ⊥ α be D, then ∠ abd = 45 ° and ∠ ACD = 30 °. Therefore, ab = √ 2a, AC = 2A
So BC = √ (AB ^ 2 + AC ^ 2) = (√ 6) a
In the rectangular coordinate system, the coordinate of point o 'is (2,0), the intersection of circle O' and X axis is at the origin O and the three points a, B, C and D are (- 1,0) (0,3) (0, b) respectively
(1) Find the analytic formula of the coordinate of point a and the straight line passing through two points BC
(2) When the point e moves on the line OC, which kinds of positional relations exist between the line be and the circle O ', and the value range of B for each positional relation is obtained
Answer by tomorrow morning! I'm useful! Process can be abbreviated, not without!
Answer by tomorrow morning! I'm useful! Process can be abbreviated, not without!
Answer by tomorrow morning! I'm useful! Process can be abbreviated, not without!
Sorry for the mistake! D is the e picture
First of all, e and D in the title should be the same. (it should be a clerical error) (1). Because OA is the diameter, so OA = 4. So a (4,0) because C (0,3) can be set as: y = KX + 3 generation B (- 1,0) get & nbsp; 0 = - K + 3 solution: k = 3. So the analytical formula of straight line through BC is: y = 3x + 3 (...)
As shown in the figure. In the rectangular coordinate system, we know point a (0,2) and point B (3,2). Please determine point C on the x-axis so that △ ABC is based on ab
Connect AB, take the middle point, make a vertical line, intersect X axis at point C, this point is the desired point
As shown in the figure, ∠ BAC = 120 °, ab = AC, BC = 4 in △ ABC, please establish an appropriate rectangular coordinate system and write out the coordinates of points a, B, C
The answer is not unique, it can be: as shown in the figure, take the straight line where BC is located as the x-axis, the vertical bisector of BC as the y-axis, and the intersection of the vertical bisector and BC as the origin to establish a rectangular coordinate system; ∵ ∠ BAC = 120 ° AB = AC, so the y-axis must pass through point a, ∵ ∠ BCA = ∠ ABC = 30 °, Bo = OC = 12bc = 2, ∵ in RT △ AOC, OA =
Given the points a (- 1,2), B (2, √, 7) (1), find the point P on the x-axis, so that the absolute value of PA = the absolute value of Pb, and find the absolute value of PA
(2) Find the point P on the x-axis so that the absolute value of PA + the absolute value of Pb is the minimum
(3) Find the point P on the x-axis so that the absolute value of Pb - the absolute value of PA takes the maximum
Let P (m, 0) (1) (M + 1) ^ 2 + 2 ^ 2 = (m-1) ^ 2 + 7, M = 1 ∩ PA absolute value = (1 + 1) ^ 2 + 2 ^ 2 = 8 (2) be the symmetric point m (- 1, - 2) of a about X axis, and connect BM ∩ X axis to a point, which is p. let BM: y = KX + B, then - 2 = - K + B, root 7 = 2K + B, and get k = (root) ∩ X axis
What is the condition of x = y
Necessary and insufficient conditions
Given that the point P (a, b) is the point of the second quadrant in the plane rectangular coordinate system, the result of simplifying | A-B | + | B-A | is ()
A. -2a+2bB. 2aC. 2a-2bD. 0
∵ point P (a, b) is the point of the second quadrant in the plane rectangular coordinate system, ∵ a ＜ 0, B ＞ 0, ∵ A-B | + | B-A | = - A + B + B-A = - 2A + 2B
RELATED INFORMATIONS
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- 2. 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?
- 3. In the plane rectangular coordinate system, as shown in Figure 1, translate the line AB to the line CD, and connect AC and BD. (1) directly write out the equal line segments and parallel lines in the figure
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- 8. P is a point outside the plane where △ ABC is located. If △ ABC and △ PBC are regular triangles with side length 2, PA = 6, then the dihedral angle p-bc-a is______ °．
- 9. Straight line and plane vertical exercises The triangle ABC has a point p outside the plane α, through which PQ is made, the vertical plane α is made, and the perpendicular foot is O, connecting PA, Pb and PC (1) If PA = Pb = PC, then o is triangular ABC___ Heart (2) If PA vertical Pb, Pb vertical PC, PC vertical PA, then o is triangular ABC___ Heart (3) If the distances from P to three sides AB, BC and Ca are equal, then o is a triangle ABC___ Heart (4) If PA = Pb = PC, ∠ C = 90 °, then o is ab edge___ . (5) If PA = Pb = PC, ab = AC, then point O is at___ on-line. There is no picture in the original question. Yes, please send me the answer and the answer
- 10. When is it necessary to make auxiliary lines and when is it not necessary to make auxiliary lines?
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- 12. As shown in the figure, point B is on line ad, C is the midpoint of line BD, ad = 10, BC = 3. Find the length of line CD and ab
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- 16. Does the origin belong to the axis?
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