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