VECTOR ALGEBRA | ADDITION OF VECTOR, SUBTRACTION OF VECTORS | Parallelogram law of addition of vectors, Properties of addition of vectors, Magnitude of addition of two vectors, Commutative law, Associative law, Existence of additive identity, Existence of additive inverse, ABC is a triangle and P any point on BC. If `barPQ` is the sum of `barAP + barPB + barPC`; show that `ABQC` is a parallelogram and `Q` therefore; is a fixed point., Addition of vectors in 3 dimensional space, ABCD is a parallelogram. E; F are mid point of BC; CD respectively. AE; AF meet the diagonal BD at points Q and P respectively. Show that points P and Q trisect DB., Subtraction of vectors, If sum of two unit vectors is a unit vector; prove that the magnitude of their difference is `sqrt3`, Let O be the centre of a regular hexagon ABCDEF. Find the sum of the vectors `OA`,` OB, OC, OD, OE` and `OF`