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 |).