⁦Equations of a line and a plane in space⁩

⁦This studio is for students who have met vectors in space⁩. ⁦It is not in Afghanistan⁩'⁦s Year 11 book; it follows Syria⁩'⁦s Year 12 book, Iran⁩'⁦s Year 12 geometry 3 and UK Further Maths⁩. ⁦A line in space is written r = a + td⁩: ⁦a is the position vector of a point on the line, d is a direction vector and t is any real number⁩. ⁦Each t gives one point of the line⁩.

⁦A plane is fixed by one of its points and a normal vector n, perpendicular to the plane⁩. ⁦A point P is on the plane if the vector from the fixed point to P is perpendicular to n, that is n·r = n·a⁩. ⁦In Cartesian form⁩: ⁦Ax + By + Cz = D, where (A، B، C) is n⁩.

⁦Common mistakes⁩: ⁦starting from B instead of A, losing the minus signs of components, and adding the components instead of multiplying them in a scalar product⁩.