Question

Three vectors $\vec{p},\vec{q}\ \text{and}\ \vec{r}$ are given as
$\vec{p}=\hat{i}+\hat{j}+\hat{k}$
$\vec{q}=\hat{i}+2\hat{j}+3\hat{k}$
$\vec{r}=2\hat{i}+3\hat{j}+4\hat{k}$
Which of the following is/are CORRECT ?

• A. $\vec{p}×(\vec{q}×\vec{r})+\vec{q}×(\vec{r}×\vec{p})+\vec{r}×(\vec{p}×\vec{q})=\vec{0}$
• B. $\vec{p}×(\vec{q}×\vec{r})=(\vec{p}.\vec{r})\vec{q}-(\vec{p}.\vec{q})\vec{r}$
• C. $\vec{p}×(\vec{q}×\vec{r})=(\vec{p}\times\vec{q})\times\vec{r}$
• D. $\vec{r}.(\vec{p}\times\vec{q})=(\vec{q}\times\vec{p}).\vec{r}$

Answer 1

Answer: (A), (B)

$\vec{p}×(\vec{q}×\vec{r})+\vec{q}×(\vec{r}×\vec{p})+\vec{r}×(\vec{p}×\vec{q})=\vec{0}$

Answer 2

The correct option is (A) : $\vec{p}×(\vec{q}×\vec{r})+\vec{q}×(\vec{r}×\vec{p})+\vec{r}×(\vec{p}×\vec{q})=\vec{0}$ and (B) : $\vec{p}×(\vec{q}×\vec{r})=(\vec{p}.\vec{r})\vec{q}-(\vec{p}.\vec{q})\vec{r}$