Home › Collection › Exam exercises › Combined exam exercise

Combined exam exercise

Given plane α (normal (2, 1, 2), constant -50), line r (through A(11, 7, 3), direction (5, 4, 6)) and point P(13, 5, 4): find the intersection of r with α, the distance from P to α and the angle between r and α.

Step-by-step solution

1. Put r inside an auxiliary projecting plane and find its intersection with α.
2. Where that intersection cuts r is I.
3. Draw through P the perpendicular to α, find the foot F and measure PF in true length.
4. The angle between r and α is the complement of the angle between r and the normal.

Result: I(13.88, 9.31, 6.46); distance PF = 3.67 u; angle r-α = 80.99°.

In a combined exercise each result builds on the previous one: if the intersection is wrong, the distance and angle are wrong too.

PractiseBack to the block