The value of the points at which intersection of plane takes place is (x,y,z) = (4,3,3).
According to the statement
we have to find the point which they intersect the given plane.
So, For this purpose, we know that the
The given equations is :
x = 5 − t, -(1)
y = 2 + t, -(2)
z = 3t -(3)
And the given plane is :
x − y + 4z = 13 -(4)
And, the intersection of plane point is :
Put the equations 1 and 2 and 3 in the 4th equations then
(5 − t) - (2 + t) + 4(3t) = 13
3 - 2t + 12t = 13
3 + 10t = 13
10t = 10
Then
t = 1
Put these values in 1 and 2 and 3rd equation then the value of x y z become
x = 5 − t, -(1)
x = 5 -1
x = 4
And
y = 2 + t, -(2)
y = 2 + 1
y = 3
And
z = 3t -(3)
z = 3(1)
z = 3.
The value of (x,y,z) = (4,3,3).
So, The value of the points at which intersection of plane takes place is (x,y,z) = (4,3,3).
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