Let \( \vec{a} \) be any vector such that \( \vec{a}\cdot\hat{\imath}=\vec{a}\cdot(\hat{\imath}+\hat{\jmath})=\vec{a}\cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=1 \), then \( \vec{a} \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \hat{\imath} \)
Let \( \vec{a}=p\hat{\imath}+q\hat{\jmath}+r\hat{k} \). The three dot products give
\( p=1 \)
\( p+q=1 \)
\( p+q+r=1 \)
So p = 1, q = 0 and r = 0, which gives \( \vec{a}=\hat{\imath} \).