MathsJEE Main 24 Jan 2026, Shift 2·Q19·MCQ·Moderate

Vectors · Vector cross product equations

Let

\vec a = 2\hat i - 5\hat j + 5\hat k

and

\vec b = \hat i - \hat j + 3\hat k

. If

\vec c

is a vector such that

2\left(\vec a\times\vec c\right) + 3\left(\vec b\times\vec c\right) = \vec 0 \quad\text{and}\quad \left(\vec a - \vec b\right)\cdot\vec c = -97,

then

\left\lvert\vec c\times\hat k\right\rvert^2

is equal to

(1)193
(2)233
(3)218
(4)205

We corrected a printing error in the original paper

Source printed “ $2\hat i - 5\hat j + 5k$ ”, “ $\hat i - \hat j + 3k$ ” and “ $\lvert\vec c\times k\rvert^2$ ” (unit vector $\hat k$ printed without its hat).

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Vectors · Vector cross product equations

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