SUMMARY

SUMMARY . For a given set of three vectors a , b and c , the scalar( c is called a scalar triple product of a , b , . . The volume of the parallelepiped formed by using the three vectors , , and a b c as co-terminus edges is given by ( c . . The scalar triple product of three non-zero vectors is zero if and only if the three vectors are coplanar . . Three vectors  a b c , , are coplanar, if, and only if there exist scalars r s t , , Î  such that atleast one of them is non-zero and ra sb tc = . . If , , a b c  and , , p q r  are any two systems of three vectors, and if p  , x a y b z c q , x a y b z c and, r x a y b z c , then , , p q r  , , a b c  . For a given set of three vectors a , b , c , the vector c is called vector triple product . . For any three vectors , a b c we have       a c b a b c ) . . Parametric form of the vector equation of a straight line that passes through a given point with position vector  a and parallel to a given vector b is tb , where ∈  . Cartesian equations of a straight line that passes through the point ( x y z and parallel to a vector with direction ratios b b b are . Any point on the line is of the form ( tb tb tb ∈  . Parametric form of vector equation of a straight line that passes through two given points with position vectors  a and b is t b a , ∈  . Cartesian equations of a line that passes through two given points ( x y z and ( are z . . If θ is the acute angle between two straight lines sb and td , then −      b d b d . Two lines are said to be coplanar if they lie in the same plane. . Two lines in space are called skew lines if they are not parallel and do not intersect . The shortest distance between the two skew lines is the length of the line segment perpendicular to both the skew lines. . The shortest distance between the two skew lines sb and td is δ =