Question bank/JEE Main/Mathematics

Let [IMAGE] and [IMAGE]. If
[IMAGE] is a vector such that [IMAGE] and
the angle between [IMAGE] and [IMAGE] is
30º, then the magnitude of the vector [IMAGE] is:
ekuk [IMAGE] rFkk rFkk chp 30° s.k gS, rks

A1.5B1.2C1.6D1.9

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1.5
[IMAGE] Now vc,
$\left| \left( \overrightarrow{x} \times \overrightarrow{y} \right) \times \overrightarrow{z} \right|$^2=
$\left| \overrightarrow{x} \times \overrightarrow{y} \right|^{2}\sin^{2}30{^\circ}$
$\left| \left( \overrightarrow{x} \times \overrightarrow{y} \right) \right|\sin{30{^\circ}} \Rightarrow \overrightarrow{x} \times \overrightarrow{y} = \left| \begin{matrix}
î & ĵ & ƙ \\
2 & 1 & - 2 \\
1 & 1 & 0
\end{matrix} \right| = 2î$+2ĵ+ƙ

Source: Grass-G / M-21 Mathematics Paper 19 Dec Hindi Eng.docx