iran-konkur 2022 Q142

iran-konkur · Other · konkur-riazi_1401_specialized Vectors Introduction & 2D Magnitude of Vector Expression
142- Three vectors $\vec{a} = (1,1,0)$, $\vec{b} = (-1,2,0)$, and $\vec{c}$ are non-coplanar, and $\vec{h} = (x,y,4)$ is the altitude vector of the parallelepiped formed by these three vectors. If $\vec{a} \cdot \vec{c} = 1$ and $\vec{b} \cdot \vec{c} = 5$, what is the magnitude of vector $\vec{c}$?
(4) $\sqrt{21}$ (3) $\sqrt{19}$ (2) $4$ (1) $5$
\textbf{142-} Three vectors $\vec{a} = (1,1,0)$, $\vec{b} = (-1,2,0)$, and $\vec{c}$ are non-coplanar, and $\vec{h} = (x,y,4)$ is the altitude vector of the parallelepiped formed by these three vectors. If $\vec{a} \cdot \vec{c} = 1$ and $\vec{b} \cdot \vec{c} = 5$, what is the magnitude of vector $\vec{c}$?

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(4) $\sqrt{21}$ \hfill (3) $\sqrt{19}$ \hfill (2) $4$ \hfill (1) $5$

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