taiwan-gsat 2024 Q18

taiwan-gsat · Other · gsat__math-a 3 marks Vectors: Lines & Planes Perpendicular/Orthogonal Projection onto a Plane

In coordinate space, let $O$ be the origin and $E$ be the plane $x - z = 4$.
If the projection of the origin $O$ onto plane $E$ is point $Q$, and the angle between vector $\overrightarrow{OQ}$ and vector $(1, 0, 0)$ is $\alpha$, what is the value of $\cos\alpha$? (Single choice question, 3 points)
(1) $-\frac{\sqrt{2}}{2}$
(2) $-\frac{1}{2}$
(3) $\frac{1}{2}$
(4) $\frac{\sqrt{2}}{2}$
(5) $\frac{\sqrt{3}}{2}$

In coordinate space, let $O$ be the origin and $E$ be the plane $x - z = 4$.

If the projection of the origin $O$ onto plane $E$ is point $Q$, and the angle between vector $\overrightarrow{OQ}$ and vector $(1, 0, 0)$ is $\alpha$, what is the value of $\cos\alpha$? (Single choice question, 3 points)\\
(1) $-\frac{\sqrt{2}}{2}$\\
(2) $-\frac{1}{2}$\\
(3) $\frac{1}{2}$\\
(4) $\frac{\sqrt{2}}{2}$\\
(5) $\frac{\sqrt{3}}{2}$

Paper Questions

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