An ant starts from a, crawls along the polygon for a week and returns to point a, then vector AB + vector BC + vector CD + vector de + vector EF + vector FG + vector GA = ()

It is a zero vector, which is only related to the starting point and end point, and has nothing to do with the process

Vector AB + (BC + CD + de)

Equal to AE

In tetrahedral a-bcd, ad = BC and ad ⊥ BC, e and F are the midpoint of AB and CD respectively, then the angle between EF and BC is

Make FG through F, parallel BC, intersect BD with G, connect Ge, EF. Ge = gf are both median lines and vertical, and the angle should be 45

It is known that in tetrahedral a-bcd, e and F are the midpoint of AB and CD respectively. If the angle formed by BD and AC is 60 ° and BD = AC = 1, find the length of EF Take the midpoint o of BC and connect OE and of. Because OE ‖ AC and of ‖ BD, ∠ EOF is the angle formed by AC and BD or its complementary angle. The problem is not that it has been told that the angle formed by the different plane straight lines BD and AC is 60 °, so the included angle of the two intersection lines after translation is 60 °, why is it still possible to be its complementary angle?

Analysis,
The included angle between the out of plane straight line BD and AC is 60 °, because the value range of the included angle of the out of plane straight line is (0, π / 2]
The included angle of two straight lines transferred to a plane is still 60 °
However, ∠ EOF may or may not be the included angle of two straight lines
∠ EOF = 60 °, or ∠ EOF = 120 °
So there are two answers,

In tetrahedral ABCD, e and F are the midpoint of edges AC and BD respectively; Vector AB + vector CB + vector AD + vector CD = 4 vector EF

Why don't vertices be capitalized?
Because e and F are the midpoint of AC and BD respectively, AE = EC, BF = FD,
Therefore, EF = EA + AB + BF, EF = EC + CD + DF,
Add the two formulas to get 2ef = (EA + EC) + (AB + CD) + (BF + DF) = AB + CD,
Because CB + ad = CB + (AC + CD) = (AC + CB) + CD = AB + CD,
So AB + CB + AD + CD = 2 (AB + CD) = 4ef

As shown in the figure, in the regular tetrahedron a-bcd (the length of the four sides of the spatial quadrilateral and the length of the two diagonals are equal), e and F are the midpoint of the edges AD and BC respectively, then the size of the angle formed by EF and AC is __

As shown in the figure, take the midpoint g of AB and connect FG and eg
Then ∠ GEF is the angle between the straight line EF and the straight line AC,
EG=1
2BD，FG=1
2AC，
∵BD=AC∴EG=FG，
The lengths of the four sides and the two diagonals of a spatial quadrilateral are equal
‡ AC ⊥ BD, i.e. eg ⊥ FG, ∠ GEF = 45 °,
So the answer is 45 °

An ant starts from a, crawls along the polygon for a week and returns to point a, then vector AB + vector BC + vector CD + vector de + vector EF + vector FG + vector GA = ()