Question:
if p(1,y,z) lies on the points (3,2,-1) and (-4,6,3) , find y
Answer:
Cartesian equation of a line that passes through two points (x1 , y1 , z1 ) and
(x2 , y2 , z2 ) is given as
(x - x1 )/(x2 - x1 ) = (y - y1 )/(y2 - y1 ) = (z - z1 )/(z2 - z1 )
Given, two points are (3, 2, -1) and (-4, 6, 3)
Now, equation of line is
(x - 3)/(-4 - 3) = (y - 2)/(6 - 2) = (z + 1)/(3 + 1)
=> (x - 3)/(-7) = (y - 2)/4 = (z + 1)/4
Again given that point p(1, y, z) lies on this line,
So, (1 - 3)/(-7) = (y - 2)/4 = (z + 1)/4
=> (-2)/(-7) = (y - 2)/4 = (z + 1)/4
=> 2/7 = (y - 2)/4 = (z + 1)/4
Now, (y - 2)/4 = 2/7
=> y - 2 = (2 * 4)/7
=> y - 2 = 8/7
=> y = 2 + 8/7
=> y = 22/7
So, the value of y is 22/7
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