Calculate the scalar product of the following vectors.
Given three forces $M = {3, - 4, 2}, W = {2, 3, - 5}, a n d P = {- 3, - 2, 4}$ applied to the same point. Calculate the work performed by the resultant of these three forces when the point of application of the resultant moves along a straight line and is displaced from the position $M_{1} {5, 3, - 7}$ to the position $M_{2} {4, - 1, - 4} .$

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Solution

The resultant of $\to M, \to W, \to P$ be $\to R$
$\to R = \to M + \to W + \to P$
$\to R = 2 \to i - 3 \to j + \to k$
$\to S = {\to S}_{2} - {\to S}_{1} = - 1 \to i - 4 \to j + 3 \to k$
$W o r k d o n e = \to R . \to S = (2 \to i - 3 \to j + \to k) . (- \to i - 4 \to j + 3 \to k) = - 2 + 12 + 3 = 13$

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