Three Dimensional Geometry Question 79
Question: For the line $ \frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} $ , which of the following is incorrect?
Options:
A) It lines in the plane $ x-2y+z=0 $
B) It is same as line $ \frac{x}{1}=\frac{y}{2}=\frac{z}{3} $ .
C) It passes through (2, 3, 5).
D) It is parallel of the plane $ x-2y+z-6=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] (1, 2, 3) satisfies the plane $ x-2y+z=0 $ and $ (\hat{i}+2\hat{j}+3\hat{k})\cdot (\hat{i}-2\hat{j}+\hat{k})=0 $ Since the lines $ \frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} $ and $ \frac{x}{1}=\frac{y}{2}=\frac{z}{3} $ both satisfy (0, 0, 0) and (1, 2, 3) both are same. Given line is obviously parallel to the plane $ x-2y+z=6. $
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