Important Points to be Remembered
( i ) Let a = a1i + a2j + a3k and b = b1i + b2j + b3k
( ii ) If a = b or if a is parallel to b , then sin θ = 0 and so a * b = 0 .
( iii ) The direction of a * b is regarded positive , if the rotation from a to b appears to be anticlockwise .
( iv ) a * b is perpendicular to the plane , which contains both a and b . Thus , the unit vector perpendicular to both a and b or to the plane containing is given by n = a * b / | a * b | = a * b / ab sin θ
( v ) Vector product of two parallel or collinear vectors is zero .
( vi ) If a * b = 0 , then a = O or b = 0 or a and b are parallel on collinear .
( vii ) Vector Product of Two Perpendicular Vectors
If θ = 900 , then sin θ = 1 , i . e . , a * b = ( ab ) n or | a * b | = | ab n | = ab