taiwan-gsat 2010 Q11

taiwan-gsat · Other · gsat__math Vectors 3D & Lines MCQ: Distance or Length Optimization on a Line

11. In coordinate space, the point on line $L$ closest to point $Q$ is called the projection of $Q$ onto $L$. Given that $L$ is a line on the plane $2x - y = 2$ passing through the point $(2, 2, 2)$. Which of the following points could be the projection of the origin $O$ onto $L$?
(1) $(2, 2, 2)$
(2) $(2, 0, 2)$
(3) $\left(\frac{4}{5}, -\frac{2}{5}, 0\right)$
(4) $\left(\frac{4}{5}, -\frac{2}{5}, -2\right)$
(5) $\left(\frac{8}{9}, -\frac{2}{9}, -\frac{2}{9}\right)$

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11. In coordinate space, the point on line $L$ closest to point $Q$ is called the projection of $Q$ onto $L$. Given that $L$ is a line on the plane $2x - y = 2$ passing through the point $(2, 2, 2)$. Which of the following points could be the projection of the origin $O$ onto $L$?\\
(1) $(2, 2, 2)$\\
(2) $(2, 0, 2)$\\
(3) $\left(\frac{4}{5}, -\frac{2}{5}, 0\right)$\\
(4) $\left(\frac{4}{5}, -\frac{2}{5}, -2\right)$\\
(5) $\left(\frac{8}{9}, -\frac{2}{9}, -\frac{2}{9}\right)$

Paper Questions

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