Questions

For the line $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$, which one of the following is incorrect ?

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a

it lies in the plane x−2y+z=0

b

it is same as line x1=y2=z3

c

it passes through (2,3,5)

d

it is parallel to the plane x−2y+z=6

detailed solution

Correct option is C

(1,2,3) satisfies the plane x−2y+z=0 and also (i^+2j+3k),(i−2j+k)=0Since the lines x−11=y−22=z−33 and x1=y2=z3both 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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The coordinates of the point where the line through $\left(3,-4,-5\right)$ and $\left(2,-3,1\right)$ crosses the plane $2x+y+z=7$ is

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