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Question

The lines xa+dαδ=yaα=zadα+δ and xb+cβγ=ybβ=zbcβ+γ are coplanar and then equation to the plane in which they lie, is

A
x+y+z=0
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B
xy+z=0
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C
x2y+z=0
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D
x+y2z=0
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Solution

The correct option is C x2y+z=0
The lines will be coplanar
∣ ∣adb+caba+dbcαδαα+δβγββ+γ∣ ∣=0
Add 3 column to first and it becomes twice the second and hence the determinant is zero as the two columns are identical. Again the equation of the plane in which they lie is
∣ ∣xa+dyazadαδαα+δβγββ+γ∣ ∣=0
Adding 1 and 3 columns and subtracting twice the 2, we get
∣ ∣x+z2yyazad0αα+δ0ββ+γ∣ ∣=0
{α(β+γ)β(α+δ)}(x+z2y)=0
x+z2y=0

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