Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

Explanation

We know that The line passing through the points (5,1,6) and (3,4,1) is given by,

`(x−5)/(3-5)​=(y−1​)/(4−1)=(z−6)/(1−6)​`

⇒ `(x−5)/(-2)​=(y−1)/(3)​=(z−6)/(-5)=k (say)`

=` x=5−2k,y=3k+1,z=6−5k`

as any point on the line is of the form `P(5−2k,3k+1,6−5k)`.


Also since line passes through `ZX`-plane,

So,Y−coordinate of point P will be` 0 =3k+1=0⇒k=−31​`

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