Hi can you please answer the following question for me in de

Hi, can you please answer the following question for me in detail??????

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 2. P =

Solution

for both to be intersecting, equation of line must satisfy the equation of plane
x+y-z=2
(1+t) + (2t) - (-3t) = 2
1 + t + 2t + 3t = 2
6*t = 1
t = 1/6

so point p is
x = 1+t + 1+1/6 = 7/6
y = 2t = 2*1/6 = 1/3
z = -3t = -3*1/6 = -1/2

P= (7/6 , 1/3 , -1/2)