Question

The radius vector and linear momentum are respectively given by vectors $2\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}-3\hat{j}+\hat{k}$. Then the angular momentum is

• A. $2\hat{i}-4\hat{k}$
• B. $4\hat{i}-8\hat{k}$
• C. $2\hat{i}-4\hat{j}+2\hat{k}$
• D. $4\hat{i}-8\hat{j}$

Answer 1

Answer: (B)

Given radius vector, $\vec{r}=2\hat{i}+\hat{j}+\hat{k}$ Linear momentum, $\vec{p}=2\hat{i}-3\hat{j}+\hat{k}$
As angular momentum, $\vec{L}=\vec{r}\times \vec{p}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 1& 1\\ 2& -3& 1\end{array}\right|$
$=\hat{i}(1-(-3))-\hat{j}(2-2)+\hat{k}(-6-2)=4\hat{i}-8\hat{k}$