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Vector Addition

A force F⃗=...

Question

A force $\to F = 3^i + c^j + 2^k$ acting on a particle causes a displacement $\to S = - 4^i + 2^j - 3^k$ in its own direction. If the work done is $6 J$ , then find the value of $c$ .

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Solution

$\to F = 3^i + c^j + 2^k$ and $\to S = - 4^i + 2^j - 3^k$
$W o r k = \to F . \to S$
$\Rightarrow (3^i + c^j + 2^k) . (- 4^i + 2^j - 3^k) = 6$
$\Rightarrow c = 12$

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