Find an equation for the plane containing the two (parallel) lines v_1=(0,1,-2)+t(2,3,-1) and v_2=(2,-1,0)+t(2,3,-1).

Mylo O'Moore

Mylo O'Moore

Answered question

2021-06-10

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

Answer & Explanation

nitruraviX

nitruraviX

Skilled2021-06-11Added 101 answers

We have v1=(0,1,2)+t(2,3,1) and v2=(2,1,0)+t(2,3,1) 
A=(0,1,-2), B=(2,-1,0) 
The plane containing these two lines will contain A and B and hence the vector AB=(2,-2,2) 
The cross product of AB and the direction ratio of the lines must be normal to the plane. 
n=AB×direction ratio of the line 
n=(2,2,2)×(2,3,1) 
n=[ijk222231]=4i+6j+10k 
[(x0)i+(y1)j+(z+2)n=0 
4(x0)+6(y1)+10(z+2)=0 
4x+6y+10z+14=0

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