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

The Correct Option is A, B

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) : \(\vec{p}×(\vec{q}×\vec{r})=(\vec{p}.\vec{r})\vec{q}-(\vec{p}.\vec{q})\vec{r}\)