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Question

Find the equations of the two lines through the origin which intersect the line x32=y31=z1 at an angle of π3

A
x1=y2=z1 or x1=y1=z2
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B
x1=y2=z1 or x1=y1=z2
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C
x1=y2=z1 or x1=y1=z2
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D
x1=y2=z1 or x1=y1=z2
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Solution

The correct option is D x1=y2=z1 or x1=y1=z2
Let point on line x32=y31=z1=λ ... (1)
are (3+2λ,3+λ,λ)
Equation of line which pass through origin is
x03+2λ=y03+λ=z0λ ... (2)
Angle between (1) & (2) is
cosπ3=(3+2λ)2+(3+λ)1+λ×1(3+2λ)2+(3+λ)2+λ222+12+1
On solving, we get
λ2+3λ+2=0
λ=1,2
Putting the value of λ in equation (2), we get
x1=y2=z1 or x1=y1=z2

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