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Question: Answered & Verified by Expert
If $\overrightarrow{\mathrm{F}}=(4 \hat{\mathrm{i}}-10 \hat{\mathrm{j}}) \mathrm{N}$ and $\overrightarrow{\mathrm{r}}=(-5 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}) \mathrm{m}$, then $(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}})$ is
PhysicsMathematics in PhysicsAP EAMCETAP EAMCET 2023 (15 May Shift 2)
Options:
  • A $(-20 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \mathrm{Nm}$
  • B $62 \hat{\mathrm{k}} \mathrm{Nm}$
  • C $10 \sqrt{13} \mathrm{Nm}$
  • D $38 \mathrm{Nm}$
Solution:
2210 Upvotes Verified Answer
The correct answer is: $62 \hat{\mathrm{k}} \mathrm{Nm}$
$\begin{aligned} & \overrightarrow{\mathrm{F}}=(4 \hat{\mathrm{i}}-10 \hat{\mathrm{j}}) \mathrm{N} \\ & \overrightarrow{\mathrm{r}}=(-5 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}) \mathrm{m} \\ & \overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ -5 & -3 & 0 \\ 4 & -10 & 0\end{array}\right| \\ & =\hat{\mathrm{k}}(50+12)=62 \hat{\mathrm{k}} \mathrm{Nm}\end{aligned}$

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