Let a vector a has magnitude 9. Let a vector b be such that for every (x, y) R × R-\(0,0), the vector (x a+y b) is perpendicular to the vector (6 y a-18 x b). Then the value of |a × b| is equal to:

Vector Algebra: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Morning shift · Q5828

JEE Main 202228 Jul, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let a vector

\vec{a}

has magnitude 9. Let a vector

\vec{b}

be such that for every

(x, y) \in \mathbf{R} \times \mathbf{R}-\{(0,0)\}

, the vector

(x \vec{a}+y \vec{b})

is perpendicular to the vector

(6 y \vec{a}-18 x \vec{b})

. Then the value of

|\vec{a} \times \vec{b}|

is equal to :