CBSE Class 11-science Answered
PROVE THAT SCALAR PRODUCT OF 2 PERPENDICULAR VECTORS IS ZERO
Asked by rksvikhyat | 01 Jun, 2012, 09:39: AM
Expert Answer
In Euclidean geometry, the dot product of vectors expressed in an orthonormal basis is related to their length and angle. For such a vector , the dot product is the square of the length (magnitude) of , denoted by :
If is another such vector, and is the angle between them:
This formula can be rearranged to determine the size of the angle between two nonzero vectors:
The CauchySchwarz inequality guarantees that the argument of is valid.
One can also first convert the vectors to unit vectors by dividing by their magnitude:
then the angle is given by
Answered by | 01 Jun, 2012, 09:49: AM
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