Given:

• A body is moving in the y-axis
• Force given = 3î + 5ĵ + 4k̂
• Distance covered in y axis = 5m

To find:

• Work done by the force.

Solution:

We know work done by a force is given by dot product of force and displacement.

Here

• F = 3î + 5ĵ + 4k̂
• displacement (S) = 5ĵ (since the object is moving only in y-axis)

Now,

W = F.S

=> W = (3î + 5ĵ + 4k̂).(5ĵ)

We know that same unit vectors are multiplied in a dot product and the product of different unit vectors is always zero for a dot product.

Hence:

W = (3î×5ĵ) + (5ĵ×5ĵ) + (4k̂×5ĵ)

W = 25J.

Therefore the work done by the force is 25J.

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Note:

• Work is a scalar quantity whichis obtained by the dot product of two vector quantities i.e., Force and displacement.
• Work is the only scalar physical quantity which can be zero, positive and negative as well. How? When the Force and displacement is antiparallel to each other, work comes out to be negative. When the force and displacement are exactly perpendicular to each other the work done comes to be zero and When the force and displacement are parallel to each other the work done comes out to be positive.
• W = FSCosθ (this formula proves the above point).

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