Let c be the projection vector of b = λ i + 4 k, λ > 0, on the vector a = i + 2 j + 2 k. If |a + c| = 7, then the area of the parallelogram formed by the vectors b and c is:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q223

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

Let

\vec{c}

be the projection vector of

\vec{b} = \lambda \hat{i} + 4 \hat{k}

\lambda > 0

, on the vector

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

. If

|\vec{a} + \vec{c}| = 7

, then the area of the parallelogram formed by the vectors

\vec{b}

and

\vec{c}

is:

Your answerInteger or decimal