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A constant force F = 5 i - 2 j + 4 k newtons moves a small trolley through the displacement d = 3 i…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A constant force $\vec F = 5\hat i - 2\hat j + 4\hat k$ newtons moves a small trolley through the displacement $\vec d = 3\hat i + 4\hat j + \hat k$ metres. Find the work done by the force. Then find the angle between $\vec F$ and $\vec d$ , and the part of the force that acts along the displacement.

Need a reminder? The key ideaShow

The scalar projection of $\vec a$ on $\vec b$ is $\dfrac{\vec a\cdot\vec b}{\lvert\vec b\rvert}$ , and $\lvert\vec a\rvert^2 = (\text{projection})^2 + \lvert\vec a_{\perp}\rvert^2$ . For a constant force, the work is $W = \vec F\cdot\vec d$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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