The value of $\hat i \cdot (\hat j \times \hat k) + \hat j \cdot (\hat i \times \hat k) + \hat k \cdot (\hat i \times \hat j)$ is

• $0$

• $- 1$

• $1$

• $3$

[Correct option is c]

$\hat i \cdot (\hat j \times \hat k) + \widehat j \cdot (\hat i \times \hat k) + \hat k \cdot (\hat i \times \widehat j) = \hat i \cdot \hat i + \widehat j \cdot ( - \widehat j) + \hat k \cdot \hat k$

$= \hat i \cdot \hat i - \hat j \cdot \hat j + \hat k \cdot \hat k = 1 - 1 + 1 = 1$