Alshia
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1. Question
Verify that the line with vector equation r = 2i+4j+k + t(-4i-4j-5k) lies wholly in the plane with equation 3x-2y+4z=2.
2. The attempt at a solution
r = (2-4t)i + (4+4t)j + (1-5t)k
3(2-4t)-2(4+4t)+4(1-5t) = 2
6-12t-8-8t+4-20t = 2
t = 0If t = 0, doesn't that mean that the line only intersects with the plane at 2i+4j+k? So then the line does not lie wholly on the plane. So there must be something wrong with this question.
Verify that the line with vector equation r = 2i+4j+k + t(-4i-4j-5k) lies wholly in the plane with equation 3x-2y+4z=2.
2. The attempt at a solution
r = (2-4t)i + (4+4t)j + (1-5t)k
3(2-4t)-2(4+4t)+4(1-5t) = 2
6-12t-8-8t+4-20t = 2
t = 0If t = 0, doesn't that mean that the line only intersects with the plane at 2i+4j+k? So then the line does not lie wholly on the plane. So there must be something wrong with this question.
