Find an equation for the plane containing the two (parallel)

eozoischgc

eozoischgc

Answered question

2022-01-07

Find an equation for the plane containing the two (parallel) lines
v1=(0,1,2)+t(2,3,1)
v2=(2,1,0)+t(2,3,1)

Answer & Explanation

Joseph Lewis

Joseph Lewis

Beginner2022-01-08Added 43 answers

Given:
v1=(0,1,2)+t(2,3,1)
v2=(2,1,0)+t(2,3,1)
Let A=(0,1,2), B=(2,1,0)
Thus, the plane containing these two lines will contain A and B. Hence, the vector AB=(2,2,2)
Normal to the plave shall be the cross product of AB and the direction ratio of the lines.
Thus, n=AB×direction ratio of the line
n=(2,2,2)×(2,3,1)
n=[ijk222231]=4i+6j+10k
Thus, the equation of the plane can be written as
(xo)i+(y1)j+(z+2)×n=0
4(x0)+6(y1)+10(z+2)=0
4x+6y+10z+14=0

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