Q122 / 160 · TS EAMCET 2013 · Physics

The work done in moving an object from origin to a point whose position vector is $\mathbf{r}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ by a force $\mathbf{F}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ is

  • A
    1 unit
  • Correct answer
    B
    9 unit
  • C
    13 unit
  • D
    60 unit

Solution

We know, work done $W=\mathbf{F} \cdot \mathbf{d}$ Given, force, $\mathbf{F}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$, and position vector, $\mathbf{d}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ Using vector identify $\hat{\mathbf{i}} \cdot \hat{\mathbf{i}}=\hat{\mathbf{j}} \cdot \hat{\mathbf{j}}=\hat{\mathbf{k}} \cdot \hat{\mathbf{k}}=1$ Hence, $\mathbf{W}=\mathbf{F} \cdot \mathbf{d}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}) \cdot(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}})$ $=6-2+5=9$ units

Hence, the correct answer is option: 'B'.

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