taiwan-gsat 2022 Q3

taiwan-gsat · Other · ast__math-a 6 marks Vectors 3D & Lines Parametric Representation of a Line

In coordinate space, $O$ is the origin, and point $P$ is in the first octant with $\overline{OP} = 1$. The line $OP$ makes an angle of $45^\circ$ with the $x$-axis, and the distance from point $P$ to the $y$-axis is $\frac{\sqrt{6}}{3}$. Select the $z$-coordinate of point $P$.
(1) $\frac{1}{2}$
(2) $\frac{\sqrt{2}}{4}$
(3) $\frac{\sqrt{3}}{3}$
(4) $\frac{\sqrt{6}}{6}$
(5) $\frac{\sqrt{3}}{6}$

In coordinate space, $O$ is the origin, and point $P$ is in the first octant with $\overline{OP} = 1$. The line $OP$ makes an angle of $45^\circ$ with the $x$-axis, and the distance from point $P$ to the $y$-axis is $\frac{\sqrt{6}}{3}$. Select the $z$-coordinate of point $P$.\\
(1) $\frac{1}{2}$\\
(2) $\frac{\sqrt{2}}{4}$\\
(3) $\frac{\sqrt{3}}{3}$\\
(4) $\frac{\sqrt{6}}{6}$\\
(5) $\frac{\sqrt{3}}{6}$

Paper Questions

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