Let a = i + 2j + k and b = 2i + j - k. Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a. Then such a vector c is:

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q209

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

Let

\vec{a} = \hat{i} + 2\hat{j} + \hat{k}

and

\vec{b} = 2\hat{i} + \hat{j} - \hat{k}

. Let

\vec{c}

be a unit vector in the plane of the vectors

\vec{a}

and

\vec{b}

and be perpendicular to

\vec{a}

. Then such a vector

\vec{c}

is: