Express the vector 
as the sum of two vectors such that one is parallel to the vector 
and the other is perpendicular to 
.
how to solve such quest. plz. explain. stepwise.
hi Anandita...
juz see wat i have done...
Let the vector parallel to n( 3i + k ), and a vector perpendicular to this be of the form... xi + yj + zk.
since these two vectors on adding gives us the vector a, we can wite the following equations..
x + 3n = 5
y = -2
z + n = 5
Now, since vector xi + yj + zk is perpendicular to vector b, their dot product must be zero. Satisfying that condition we get this..
3x + z = 0
z = -3x
and now on sloving the above 3 equations we get
n = 2
x = -1
y = -2
and z = 3
Therefore the two vectors are obtained in which 6i + 2k is parallel and -i - 2j + 3k is perpendicular to vector b.
The solution obtained can also be checked :
( 6i + 2k ) + ( -i - 2j + 3k ) = 5i - 2j + 5k
which is the given a vector.