Vector Equation of Line and Plane
( i) Vector equation of the straight line passing through origin and parallel to b is given by r = t b, where t is scalar.
( ii) Vector equation of the straight line passing through a and parallel to b is given by r = a + t b, where t is scalar.
( iii) Vector equation of the straight line passing through a and b is given by r = a + t( b – a), where t is scalar.
( iv) Vector equation of the plane through origin and parallel to b and c is given by r = s b + t c, where s and t are scalars.
( v) Vector equation of the plane passing through a and parallel to b and c is given by r = a + sb + t c, where s and t are scalars.
( vi) Vector equation of the plane passing through a, b and c is r =( 1 – s – t) a + sb + tc, where s and t are scalars.
Bisectors of the Angle between Two Lines
( i) The bisectors of the angle between the lines r = λa and r = μb are given by r = & lamba;( a /
| a | & plumsn; b / | b |)
( ii) The bisectors of the angle between the lines r = a + λb and r = a + μc are given by r = a +
& lamba;( b / | b | & plumsn; c / | c |).