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A plane passes through the two points (3, 4, 1) and (0, 1, 0) and is parallel to the line (x + 3)/2 = (y - 3)/7 = (z - 2)/5. If the equation of this plane can be written as 8x - 13y + 5*lambda*z + 13 = 0, find the value of lambda.
- lambda = 1
- lambda = 2
- lambda = 3
- lambda = 5
Correct answer: lambda = 3
Solution
The cross product of the vector (3, 3, 1) and the line direction (2, 7, 5) gives the normal (8, -13, 15). Comparing 15z with 5*lambda*z yields lambda = 3.
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