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Question

Find the components of a=2^i+3j along the directions of vectors ^i+^j and ^i^j:

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Solution

Let the given vector be
a=2^i+3^j
To find the component of 'a' along ^i+^j we have to find unit vector along ^i+^j
Let the unit vector be ^a

^a=^i+^j|^i+^j=12(^i+^j)
Component of a along ^i+^j
=(a^a)^a

=[(2^i+3^j)12(^i+^j)]12(^i+^j)

=[12(2+3)]12(^i+^j)

=52[12(^i+^j)]

=52^i+52^j

Component of a along ^i^j
=(a^a)^a

=[(2^i+3^j)12(^i^j)]12(^i^j)

=[12(23)]12(^i^j)

=12[12(^i^j)]

=12^i+12^j


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