Solution

The correct answer is (A), (C) and (D) Only

EXPLANATION:

We can determine whether one point obscures another by examining the lines formed from the view point (C) to each point in question. Specifically, we need to find whether the given points (P1, P2, P3) are on the same line (i.e., they are collinear) formed with view point C. If the points are collinear, the point that is closer to the view point will obscure the farther one when seen from the view point.

The vector SOa formed by Segment OC, in this case, is directed from point O to point a in 3D space. If P1, P2, P3 and C are collinear, then vector CP1 = a1 * CP2, vector CP1 = a2 * CP3 and vector CP2 = a3 * CP3.

Let's calculate these vectors and check:

• Vector CP1: (1 - 0, 2 - 0, 0 - -10) = (1, 2, 10) Vector CP2: (3 - 0, 6 - 0, 20 - -10) = (3, 6, 30) Vector CP3: (2 - 0, 4 - 0, 6 - -10) = (2, 4, 16)

We can say that one vector is a scalar multiple of the another vector if all components are multiplied by the same scalar value. Therefore,

• CP2 = 3CP1 since (3, 6, 30) = 3(1, 2, 10)
• CP3 ≠ any multiple of CP1, or of CP2 as (2, 4, 16) ≠ any multiple of (1, 2, 10) or (3, 6, 30)

So, from point C,

• (A) P1 obscures P2, as P2 lies on the line segment from C to P1.
• (B) P2 does not obscure P1, as P1 is nearer to C on the same line segment.
• (C) P3 does not obscure P1, as they do not lie on the same line segment.
• (D) P2 does not obscure P3, as they do not lie on the same line segment.

So, the correct answer is: (A), (C) and (D) Only