Find the coordinates of the point where the line through `(3, 4, 5)`and `(2, 3, 1)`crosses the plane`2x + y + z = 7`.

Explanation

We know that the equation of the line passing through the point (x1​,y1​,z1​) and (x2​,y2​,z2​) is
`(​x−x_1​​)/(x_2​−x_1)=(​y−y_1​​)/(y_2​−y_1)=(​z−z1​​)/(z_2​−z_1)`

As line given passes through the points (3,4,5) and (2,3,1)

So, the equation of the line is

`(x−3)/(2−3)​=(y-4)/(3-4)​=(z-5)/(1-5)​`

⇒`(x−3)/(-1)​=(y-4)/(-1)​=(z-5)/(-4)​=k(say)`

On simplifying we get `x−3=−k,y-4=-k,z-5=-4k`

⇒`x=−k+3,y=-k+4,z=-4k+5`

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