VECTOR ALGEBRA | DOT PRODUCT, PROPERTIES OF DOT PRODUCT, APPLICATIONS OF DOT (SCALAR) PRODUCT | Definition; remarks and geometrical interpretation of Scalar Product, `a.a = |a|^2` and commutative and distributive law of dot product, `l veca . m vecb = lm(veca . vecb)` and `veca . vecb = 0` then `veca` and `vecb` are perpendicular if `veca` and `vecb` are not null vector, `|veca pm vecb|^2 = |veca|^2 + |vecb|^2 pm 2|veca||vecb|cos theta` and `(veca + vecb).(veca - vecb) = |veca|^2 - |vecb|^2`, Dot product in terms of components, Using dot product of vectors; prove that a parallelogram; whose diagonal are equal; is a rectangle., Angle between two vectors in terms of dot product, Components of vector along and perpendicular a vector, Cosine rule using dot product, Prove by vector method that `cos(A+B) = cosAcosB - sinAsinB`