A force $\vec{F}=2 \hat{i}+b \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displaceme

Question

A force $\vec{F}=2 \hat{i}+b \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$. What will be the value of $b$, if work done on the particle is zero?\

Professor PC Thomas Classes · Answer

(d) : $\vec{F}=2 \hat{i}+b \hat{j}+\hat{k}, \vec{s}=\hat{i}-2 \hat{j}-\hat{k}$ $$ \begin{aligned} & W=0 \Rightarrow \vec{F} \cdot \vec{s}=0 \ \Rightarrow \quad & (2 \hat{i}+b \hat{j}+\hat{k}) \cdot(\hat{i}-2 \hat{j}-\hat{k})=0 \end{aligned} \ \begin{array}{ll} \Rightarrow & 2-2 b-1=0 \ \Rightarrow & 1=2 b \Rightarrow b=1 / 2 \end{array} $$