A particle acted on by constant forces f¯$$=4i^+3j^-3k^$$ and g→$$=3i^+j^-k^$$ experiences a displacement from the point a→$$=i^+2j^+3k^$$ to the point b→$$=5i^+4j^+k^$$ . The total work done by the forces is

Resultant F→$$=7i^+4j^$$−$$4k^d$$→$$=(5i^+4j^+k^)$$−(i^+2j^+3k^)=4i^+2j^$$−$$2k^$$∴$$W=F$$→⋅d→ $$=(7i^+4j^$$−$$4k^)(4i^+2j^$$−$$2k^) $$=28+8+8=44$$

Dot product or scalar product of vectors

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Question

$A particle acted on by constant forces \bar{f} = 4 \hat{i} + 3 \hat{j} - 3 \hat{k}$ $and \vec{g} = 3 \hat{i} + \hat{j} - \hat{k} experiences a displacement from the$ $point \vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k} to the point \vec{b} = 5 \hat{i} + 4 \hat{j} + \hat{k} . The total$ $work done by the forces is$

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Solution

$\begin{matrix} Resultant \vec{F} = 7 \hat{i} + 4 \hat{j} - 4 \hat{k} \\ \vec{d} = (5 \hat{i} + 4 \hat{j} + \hat{k}) - (\hat{i} + 2 \hat{j} + 3 \hat{k}) = 4 \hat{i} + 2 \hat{j} - 2 \hat{k} \\ ∴ W = \vec{F} \cdot \vec{d} \\ = (7 \hat{i} + 4 \hat{j} - 4 \hat{k}) (4 \hat{i} + 2 \hat{j} - 2 \hat{k}) \\ = 28 + 8 + 8 = 44 \end{matrix}$

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Dot product or scalar product of vectors

Remember concepts with our Masterclasses.

A particle acted on by constant forces f¯=4i^+3j^-3k^ and g→=3i^+j^-k^ experiences a displacement from the point a→=i^+2j^+3k^ to the point b→=5i^+4j^+k^ . The total work done by the forces is

Resultant F→=7i^+4j^−4k^d→=(5i^+4j^+k^)−(i^+2j^+3k^)=4i^+2j^−2k^∴W=F→⋅d→ =(7i^+4j^−4k^)(4i^+2j^−2k^) =28+8+8=44

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