Video tutorials - Section formula Mathematics CBSE (Arts)

Find the coordinate of the point P where the line through A(3, –4, –5) and B(2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0).
Also, find the ratio in which P divides the line segment AB.

In a quadrilateral ABCD, prove that \[{AB}^2 + {BC}^2 + {CD}^2 + {DA}^2 = {AC}^2 + {BD}^2 + 4 {PQ}^2\] where P and Q are middle points of diagonals AC and BD. 

If the median to the base of a triangle is perpendicular to the base, then triangle is isosceles. 

If AD is the median of ∆ABC, using vectors, prove that \[{AB}^2 + {AC}^2 = 2\left( {AD}^2 + {CD}^2 \right)\] 

Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square. 

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `(2veca + vecb)` and `(veca - 3vecb)` externally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.

Prove that the diagonals of a rhombus are perpendicular bisectors of each other. 

Prove using vectors: The quadrilateral obtained by joining mid-points of adjacent sides of a rectangle is a rhombus.