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1.
If 
, then 
equals
, then equals
2.
In a parallelogram 
and 
. The value of 
is
and . The value of is
3.
If 
be the angle between the vectors 
and 
, then
be the angle between the vectors and , then
4.
Let 
be three non-zero vectors such that no two these are collinear. If the vector 
is collinear with 
is collinear with 
(λ being some non-zero scalar). Then 
equals
be three non-zero vectors such that no two these are collinear. If the vector is collinear with is collinear with (λ being some non-zero scalar). Then equals
5.
Let 
be a triangle the position vectors of whose vertices are respectively 
and 
. Then, 
is
be a triangle the position vectors of whose vertices are respectively and . Then, is
6.
7.
If 
are non-coplanar vectors and λ be a real number, then the vectors 
and 
are non-coplanar for
are non-coplanar vectors and λ be a real number, then the vectors and are non-coplanar for
8.
The position vectors of 
and 
are respectively 
and 
.If R is a point on 
such that 
then the position vector of 
is
and are respectively and .If R is a point on such that then the position vector of is
9.
Let 
be unit vectors. Suppose 
and the angle between 
and 
. Then, 
be unit vectors. Suppose and the angle between and . Then,
10.
If 
and 
are the position vectors of the points A and B , then the position vector of the points of trisection of AB are
and are the position vectors of the points A and B , then the position vector of the points of trisection of AB are