Prove that l 1 is parallel to l2.
Proof method: 1) First find the direction vectors A and B of the straight line l 1 and the straight line l2.
2) If vector a=(x, y), vector b=(m, n).
3) It is proved that vector A is parallel to vector B, that is, x=tt is a unique constant multiple of m and y = t multiple of n.
4) So l 1 is parallel to l2.
2, n points * * * surface
Prove that p is on the surface abc
Please make it clear that any three points in space can determine a plane. When proving the N-point * * * plane, what we learned in high school is actually to know three points abc, determine a plane abc, and then prove that another point P is on this plane. That is to say, we only study four aspects in senior high school. ※. ※。
Proof method:
The first category: pure geometric proof.
(1) If four points are connected into two straight lines respectively, it is a * * * plane.
(2) There is a positional relationship. For example, after two straight lines are connected into a straight line, the two straight lines are vertical and parallel.
The second category: analytic geometry proof. Suppose these four points are a, b, c and d. (No two points coincide)
Let's not talk about establishing a spatial coordinate system, just talk about the vector method.
① The basic theorem of plane vector. If vector AB and vector AC can linearly represent AD, that is, there are two real numbers α and β, then,
α vector AB+β vector AC= vector AD, then they are * * * planes.
② First find the normal vector n of plane ABC, and then multiply it by AD point. If it is equal to 0, d must be on the plane ABC.
3. Other issues
And other problems proved by vectors? This question is too general to answer.
However, to learn the vectors in solid geometry, it is very important to establish a system, express all the points that the vectors need to express, and combine the expressed vectors with the normal vectors of the plane, that is, any vectors perpendicular to the plane, so as to simply solve the problems of parallelism, verticality and included angle.
Establishing system is a very important concept in vector solid geometry.
That's my answer. I hope it helps.