۴.۵. مقدمات ریاضی | حل تست و تمرین از خط و صفحه در فضای سه بعدی

简介：

In this video, we walk through a series of exercises on lines and planes in three‑dimensional space. 00:00 – Example 1: equation of a plane given a point and a normal vector. 02:59 – Example 2: equation of a plane passing through three points. 07:36 – Example 3: equation of a plane passing through two points and perpendicular to a given plane. 12:21 – Example 4: intersection point of a line and a plane. 16:53 – Example 5: distance between two parallel planes. 19:08 – Example 6: relative position of two lines. 25:54 – Example 7: shortest distance between two lines. 29:40 – relative position of a line and a plane. 31:05 – Example 8: relative position of a line and a plane. 33:14 – Example 9: angle between a line and a plane. 34:28 – Example 10: projection of a point onto a plane.