MathsJEE Main 5 Apr 2026, Shift 1·Q14·MCQ·Moderate

Vectors · Vector cross product equations

Let

\vec a = \sqrt7\,\hat i + \hat j - \hat k

and

\vec r\times\vec a + \vec a\times\vec b = \vec 0

. If

\vec r

is a vector such that

\vec r\times\vec a + \vec a\times\vec b = \vec 0

and

\vec r\cdot\vec a = 0

, then

\lvert 3\vec r\rvert^2

is equal to:

(1)44
(2)54
(3)86
(4)132

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