Porisma

A hint to get started

Trace and reflect two rays inside a cuboid

The closed cuboid has OA = 12 cm, OC = 10 cm, OE = 5 cm. O is the origin; perpendicular unit vectors i,j,k are parallel to OA, OC, OE. Vertex order is as in the diagram.

A yellow ray starts at O in direction i+2j+2k\mathbf i+2\mathbf j+2\mathbf k. A blue ray starts at A and passes through H on ED with EH:ED=2:5.

(i) Will the yellow and blue paths cross? Explain clearly. marks

(ii) Find the angle between the blue ray and plane DEFG. marks

(iii) Find X where the yellow ray meets DEFG. marks

(iv) DEFG is reflective. The yellow ray reflects and meets OABC at Y. Find the area of triangle OXY. marks

Expand diagram

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Cuboid OABC as bottom face and EFGD as the corresponding top face: O below E, A below F, B below G, C below D. OA=12 along i, OC=10 along j, OE=5 along k; these axes are perpendicular. Hidden edges OC, CB, CD are dashed. The perspective schematic reproduces all eight source vertices; it is not a metric screen projection. H on ED is added at EH:ED=2:5 for the blue-ray construction.
Cuboid OABC as bottom face and EFGD as the corresponding top face: O below E, A below F, B below G, C below D. OA=12 along i, OC=10 along j, OE=5 along k; these axes are perpendicular. Hidden edges OC, CB, CD are dashed. The perspective schematic reproduces all eight source vertices; it is not a metric screen projection. H on ED is added at EH:ED=2:5 for the blue-ray construction.
Cuboid OABC as bottom face and EFGD as the corresponding top face: O below E, A below F, B below G, C below D. OA=12 along i, OC=10 along j, OE=5 along k; these axes are perpendicular. Hidden edges OC, CB, CD are dashed. The perspective schematic reproduces all eight source vertices; it is not a metric screen projection. H on ED is added at EH:ED=2:5 for the blue-ray construction.

[2017/AJC/MYE/J2/I/8]

CJC · Review problems · Question 14

Use the perpendicular coordinate axes supplied by the cuboid before tracing rays.

Read the worked solution