Find the angle vetween force ` vec F =(3 hat I + 4 hat j -5 hat k)` and displacement ` vec d =(5 hat I + 4 hat j + 3 hat k)` unit. Also find the projection of ` vec F along vec d`.

Explanation

To find the angle between the force vector \( \vec{F} = 3 \hat{i} + 4 \hat{j} - 5 \hat{k} \) and the displacement vector \( \vec{d} = 5 \hat{i} + 4 \hat{j} + 3 \hat{k} \), we can use the formula for the dot product:

\[ \vec{F} \cdot \vec{d} = |\vec{F}| |\vec{d}| \cos \theta \]

Where \( \theta \) is the angle between the two vectors.

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