Q220 / 270 · NDA 2016 (Phase 2) · Mathematics

A force $\vec{F}=3 \hat{i}+2 \hat{j}-4 \hat{k}$ is applied at the point $(1,-1,2)$. What is the moment of the force about the point $(2,-1,3)$ ?

  • A
    $\hat{\mathrm{i}}+4 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$
  • B
    $2 \hat{i}+\hat{j}+2 \hat{k}$
  • Correct answer
    C
    $2 \hat{i}-7 \hat{j}-2 \hat{k}$
  • D
    $2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-\hat{\mathrm{k}}$

Solution

Let point $P$ is $(1,-1,2)$ and point $Q$ is $(2,-1,3)$ $\Rightarrow$ Position vector of $P$ w.r.t. $Q$ is $\begin{aligned} & \vec{r}=(1-2) \hat{i}+(-1+1) \hat{j}+(2-3) \hat{k} \\ & \Rightarrow \vec{r}=-\hat{i}+0 \hat{j}-\hat{k} \text { and } \vec{F}=3 \hat{i}+2 \hat{j}-4 \hat{k} \\ & \Rightarrow \text { Moment }=\vec{r} \times \vec{F}=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ -1 & 0 & -1 \\ 3 & 2 & -4 \end{array}\right| \\ & =\hat{i}(0+2)-\hat{j}(4+3)+\hat{k}(-2+0)=2 \hat{i}-7 \hat{j}-2 \hat{k} \end{aligned}$

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

Relevant Questions