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Question

With respect to a rectangular cartesian co-ordinate system three vectors are expressed as a=4^i^j,b=3^i+2^j and c=^k where ^i,^j and ^k are unit vectors along the x, y, z axes respectively. The unit vector along the direction of sum of these vectors is

A
^r=13(^i+^j^k)
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B
^r=12(^i+^j^k)
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C
^r=13(^i+^j+^k)
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D
^r=13(^i+^j+^k)
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Solution

The correct option is A ^r=13(^i+^j^k)
Given, a=4^i^j,b=3^i+2^j and c=^k
Sum of these vectors,
r=a+b+c=4^i^j3^i+2^j^k
^r=r|r|=^i+^j^k12+12+(1)2
^r=^i+^j^k3

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