The area of the parallelogram of which \(\hat{\imath}\) and \(\hat{\imath}+\hat{\jmath}\) are adjacent sides is _________.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
The area of a parallelogram with adjacent sides \(\vec{a}\), \(\vec{b}\) is \(|\vec{a}\times\vec{b}|\) (cross product).
\(\hat{\imath}\times(\hat{\imath}+\hat{\jmath}) = \hat{\imath}\times\hat{\imath}+\hat{\imath}\times\hat{\jmath}\)
\(= \vec{0}+\hat{k} = \hat{k}\)
\(\text{Area} = |\hat{k}| = 1\)
The value \(\frac{1}{2}\) would be the area of the triangle on these two sides, not of the parallelogram.