Question

if x/q+r-p=y/r+p-q=z/p+q-r, prove that the value of (q-r)x+(r-p)y+(p-q)=0?​

Answer 1

Answer:

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Step-by-step explanation:

xq+r−p=yr+p−q=zp+q−r represents the line L

L→P=→v1λ with →v1=(q+r−p,r+p−q,p+q−r)

Here P=(x,y,z)

Any plane Π containing L such as

Π→⟨P,→v2⟩=0 has the property

⟨→v1λ,→v2⟩=λ⟨→v1,→v2⟩=0 for any λ∈R

so

→v1,→v2 must be orthogonal.

If we choose →v2=(q−r,r−p,p−q)

we can easily verify that ⟨→v1,→v2