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If point P is a point in the cube abcd-a'b'c'd 'with edge length 1 and AP = 3 / 4AB + 1 / 2ad + 2 / 3AA', then the distance from point P to edge length AB is_________
Take point a as the origin to establish a three-dimensional rectangular coordinate system (the three coordinate axes are AB, ad, AA ')
Then the coordinates of AP are (3 / 4,1 / 2,2 / 3)
Project point P onto add'a ',
The distance from point P to edge length AB is
Radical [(1 / 2) & sup2; + (2 / 3) & sup2;] = 5 / 6
So the distance from point P to edge length AB is 5 / 6
In the cube abcd-a1b1c1d1, the edge length is 1, and the vector method is used to calculate the distance from point C1 to A1C
Take d1a1 as X axis, d1c1 as y axis and d1d as Z axis to establish space rectangular coordinate system
Then vector A1C = (- 1,1,1), vector a1c1 = (- 1,1,0)
∴cos=(1+1+0)/（√3*√2）=√6/3
∴sin=√3/3
The distance between point C1 and A1C = a1c1 * sin = √ 6 / 3
In the trapezoidal ABCD, AD / / BC, ab = CD, AE ⊥ BC is at the point E, AE = 4AD, AC = BC, find the value of AD / BC
If the auxiliary line AF | DC intersects BC with F, there will be: △ AFC is all equal to △ CDA (it's easy to see that all three sides are equal); at the same time, △ AEB is all equal to △ AEF (right angle, common edge, ab = AF = DC), which is clear. Let ad = x, be = y, then there will be: BC = be + EF + FC = 2Y + X; then the required value is
In isosceles trapezoid ABCD, ad is parallel to BC, e is the midpoint of BC, AE and de are connected, and AE = De is calculated
Because the isosceles trapezoid ABCD, ad parallel BC
So AB = CD; angle Abe = angle DCE
Because e is the midpoint of BC
So be = EC
Because AB = CD, Abe = DCE, be = EC (SAS)
So triangle Abe congruent triangle DCE
So AE = De
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