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Question
Find the work done in moving an object along a straight line from (3,2,−1) to (2,−1,4) in a force field given by →F=4^i−3^j+2^k.
Find the work done in moving an object along a straight line from (3,2,−1) to (2,−1,4) in a force field given by →F=4^i−3^j+2^k.
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Solution
The correct option is B 15 units
Let the the object move from P(3,2,−1) to Q(2,−1,4)Here, the position vectors, →p=3^i+2^j−^k and →q=2^i−^j+4^k Hence, →PQ=→q−→p=(2^i−^j+4^k)−(3^i+2^j−^k)=−^i−3^j+5^k→F=4^i−3^j+2^k
∴ Work done =→F.→PQ =(4^i−3^j+2^k).(−^i−3^j+5^k)
=−4+9+10=15 units
Let the the object move from P(3,2,−1) to Q(2,−1,4)
Here, the position vectors, →p=3^i+2^j−^k and →q=2^i−^j+4^k
Hence, →PQ=→q−→p=(2^i−^j+4^k)−(3^i+2^j−^k)=−^i−3^j+5^k→F=4^i−3^j+2^k
∴ Work done =→F.→PQ =(4^i−3^j+2^k).(−^i−3^j+5^k)
=−4+9+10=15 units
∴ Work done =→F.→PQ =(4^i−3^j+2^k).(−^i−3^j+5^k)
=−4+9+10=15 units
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