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If PA = 8, Pb = 5 and OA: OB = 4: √ 3, then the distance from point P to plane a is equal to
Let the length of OA be x first, then the length of ob can be expressed according to the relationship between OA and OA. Then use the right triangle POA and right triangle POB, and use two Pythagorean theorems to list the equality of Po, then x can be obtained. In the reverse substitution, Po can be obtained, that is, the distance from P to plane A. without mathematical symbol input software, I don't know if you can understand it
PA, Pb and PC are three rays from point P, each of which has an angle of 60 degrees, and the cosine of the angle between PC and APB
The value is
Cos60 degree / cos30 degree = √ 3 / 3
What is the cosine of the dihedral angle a-pb-c when three rays PA, Pb and PC are drawn from a point P and they are at an angle of 60 degrees?
Please explain why,
Solution: from the title to know that each corner is 60
Therefore, each surface is a regular triangle, which is a regular three shuttle cone
Let the midpoint of AC be o, OB be the positive x-axis, OC be the positive y-axis, Op be the positive y-axis, and the side length be 1
Then: a (0, - 1 / 2,0), P (0,0, root 3 / 2), B (root 3 / 2,0,0), C (0,1 / 2,0)
The normal vector N1 = (1, - radical 3,1) of APB is obtained
The normal vector N2 of PBC = (1, root 3,1)
So cosa = N1N2 / N1 | N2 | 1 / 5
So the angle is arccos1 / 5
If three rays PA, Pb and PC are introduced from a point P in space and the three rays form an angle of 60 ° each other, then the cosine value of the plane angle of dihedral angle a-pb-c is 0
A.1/3 B.2/3 C.-1/3 D.-2/3
PA, Pb and PC can be thought of as regular triangles with all edges of 2, so that all sides are regular triangles. Remove the midpoint D of Pb and connect AD and CD, then ad and CD are perpendicular to Pb, which is called ADC dihedral angle
Ad = CD = root 3, AC = 2, so using the cosine theorem, we know the answer is a
RELATED INFORMATIONS
- 1. PA, Pb and PC are three rays from P, and the angle between each two rays is 60 degrees. So what is the cosine of the angle between PC and PAB? Which is the angle between PC and PAB and why A proof of the angle between line PC and plane PAB
- 2. We know that the line AB = 8, and there is a point P on the plane. (1) if AP = 5, what is Pb equal to, P is on the line AB?
- 3. PA, Pb and PC are three rays starting from point P. the angle between each two rays is 60 degrees. Then the cosine of the angle between PC and PAB is () A. 12B. 22C. 33D. 63
- 4. Point P is on the vertical bisector of line AB, PA = 7, then Pb=______ ．
- 5. Know a (2,1), B (1,3), find a point P on the x-axis, so that the value of PA + Pb is the minimum, then what is the minimum value?
- 6. Given the straight line L: 2x-y + 1 = 0 and the point a (- 1,2) B (0,3), try to find a point P on L, so that the value of PA = Pb is minimum, and find the minimum value
- 7. Given the points a (- 2,5) and B (2,4), find a point P on the straight line L: 2x-2y + 1 = 0, so that | PA | + | Pb |, and find the minimum value
- 8. Given the points a (- 1,0), B (1,0), P is the moving point on the line 2x-y + 1 = 0. (1) when the vector PA * and the vector Pb take the minimum value, we find the coordinates of the op vector and Co And find the value of COS angle APB (2) if P satisfies PA + Pb = pa-pb, the coordinates of P
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- 11. As shown in the figure, PA ⊸ o is in the plane, AB is the diameter of ⊙ o, C is the point on ⊙ o, and E.F is the point a in the plane PB.PC The following conclusions are given: 1, AF ⊥ Pb; 2, EF ⊥ Pb; 3, AF ⊥ BC; 4, AE ⊥ plane PBC, where the sequence number of the correct proposition is
- 12. P is a point out of plane a. the angle difference between PA, Pb and plane a is π / 4. Their projective lengths in plane are 2 and 12 respectively. The distance from P to plane is
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