iran-konkur 2018 Q133

iran-konkur · Other · konkur-riazi_1397_specialized Vectors 3D & Lines Normal Vector and Plane Equation
133- Vector $\mathbf{a}$ makes an angle of $60°$ with each of the axes $Ox$ and $Oy$, and makes a right angle with the axis $z$. This vector is perpendicular to which plane? Which equation does the plane satisfy?
(1) $x - \sqrt{2}y + z = 0$ (2) $2x + 2y + \sqrt{2}z = 0$
(4) $x + y - \sqrt{2}z = 0$ (3) $x + y + \sqrt{2}z = 0$
\textbf{133-} Vector $\mathbf{a}$ makes an angle of $60°$ with each of the axes $Ox$ and $Oy$, and makes a right angle with the axis $z$. This vector is perpendicular to which plane? Which equation does the plane satisfy?

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(1) $x - \sqrt{2}y + z = 0$ \hfill (2) $2x + 2y + \sqrt{2}z = 0$

(4) $x + y - \sqrt{2}z = 0$ \hfill (3) $x + y + \sqrt{2}z = 0$

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