NIMCET 2018 — Mathematics PYQ

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Question

NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

Forces $4 \hat{i} - 3 \hat{j} + 7 \hat{k}$ and $- 2 \hat{i} + 2 \hat{j} - 8 \hat{k}$ are acting on a particle and displaced it from the point (5, 7, 1) to (2, 5, -6), then the work done by the force is

Choose the correct answer:

Explanation

Concept:
The work done by the force is given as follows:
$W = F \cdot d$

Here, $F$ is the force vector and $d$ is the displacement vector.

Calculation:
Net force acting on the particle is calculated as follows:
$F_{1} = 4 \hat{i} - 3 \hat{j} + 7 \hat{k}$ and $F_{2} = - 2 \hat{i} + 2 \hat{j} - 8 \hat{k}$

$F = F_{1} + F_{2}$

$F = 2 \hat{i} - \hat{j} - \hat{k}$

Displacement vector is calculated as follows:

$d = (2 - 5) \hat{i} + (5 - 7) \hat{j} + (- 6 - 1) \hat{k}$

$\Rightarrow d = - 3 \hat{i} - 2 \hat{j} - 7 \hat{k}$

Now,

$W = F \cdot d$

$W = (2 \hat{i} - \hat{j} - \hat{k}) \cdot (- 3 \hat{i} - 2 \hat{j} - 7 \hat{k})$

$= - 6 + 2 + 7$

$= 3 J$

Choose the correct answer:

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