Reciprocal System of Vector
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Reciprocal System of Vector
Vector of Class 12
Reciprocal System of Vector
A vector having the same direction as that of a given vector a however the magnitude equal to the reciprocal of the given vector is known as the reciprocal of vector a.
It is denoted by a
−1
If
are three non coplanar vectors such that [
] ≠ 0, then the system of vectors
which satisfy the condition that a.a′ = b.b′ = c.c′ = 1 &
and
are called reciprocal vectors to
,
and
.
Properties of reciprocal system
(a)
(b)
(c) The system of unit vectors
is its own reciprocal
i.e.
.
Note that any vector can be expressed in terms of
as they also constitute a system of non coplanar vectors.
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