EDUCATION FOR BETTER TOMMROW
Friday, 8 August 2014
CHAPTER 17-Properties of Dot Product
From the definition of the dot product, we can make certain useful observations about its properties.
between two vectors
is given by
, the equality holding only if
The projection of
The projection of
Scalar product is commutative i.e.,
Scalar product is distributive i.e.,
The scalar product of two vectors is zero if and only if the two vectors are perpendicular.
This also gives
For any vector
This property is very important. If two vectors
have been specified in rectangular form
between the two vectors will be given by
The direction cosines
of a vector
will be given by
be a vector coplanar with the vectors
this would imply that
is perpendicular to both
. This can only happen if
be an arbitrary vector and
be three vectors such that
This means that
is perpendicular to each of
which can only happen if
be three non-coplanar vectors. We’ve already discussed that
can form a basis for
space. Any vector
can be written in this basis as
This representation is of significant importance and you must understand how it comes about.
August 08, 2014
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