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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
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
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Solution
The correct option is A ^r=1√3(^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−^j−3^i+2^j−^k
^r=→r|→r|=^i+^j−^k√12+12+(−1)2
^r=^i+^j−^k√3
Given, →a=4^i−^j,→b=−3^i+2^j and →c=−^k
Sum of these vectors,
→r=→a+→b+→c=4^i−^j−3^i+2^j−^k
^r=→r|→r|=^i+^j−^k√12+12+(−1)2
^r=^i+^j−^k√3
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