Correct Answer - Option 3 : î - ĵ + k̂
Concept:
Let \(\rm\vec{a}\) and \(\rm\vec{b}\) be the two vectors and the vector \(\rm\vec{c}\) perpendicular to both \(\rm\vec{a}\) and \(\rm\vec{b}\)
Hence \(\rm\vec{c} = \rm\vec{a} × \rm\vec{b}\)
Calculation:
Let vector \(\rm\vec{c}\) is perpendicular to both the vectors î + ĵ and ĵ + k̂
Let \(\rm \vec a \) = î + ĵ and \(\rm \vec b \) = ĵ + k̂
Therefore, \(\rm\vec{c} = \rm\vec{a} × \rm\vec{b}\)
= (î + ĵ) × (ĵ + k̂)
= î × ĵ + î × k̂ + ĵ × ĵ + ĵ × k̂
= k̂ - ĵ + 0 + î
= î - ĵ + k̂