The value of \(\hat{\imath}\cdot\left(\hat{k} \times \hat{\jmath}\right) + \hat{\jmath}\cdot\left(\hat{\imath} \times \hat{k}\right) + \hat{k}\cdot\left(\hat{\jmath} \times \hat{\imath}\right)\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −3
In the cyclic order \(\hat{\imath} \to \hat{\jmath} \to \hat{k} \to \hat{\imath}\), a cross product taken in the cyclic order is positive and in the reverse order is negative. All three products here are in the reverse order:
\(\hat{k} \times \hat{\jmath} = -\hat{\imath}\)
\(\hat{\imath} \times \hat{k} = -\hat{\jmath}\)
\(\hat{\jmath} \times \hat{\imath} = -\hat{k}\)
So the expression is
\(\hat{\imath}\cdot(-\hat{\imath}) + \hat{\jmath}\cdot(-\hat{\jmath}) + \hat{k}\cdot(-\hat{k})\)
\(= -1 - 1 - 1 = -3\)
Note: This topic was not in the CUET 2026 syllabus.