1
Question
If the lines
x−21=y−31=z−4λ and
x−1λ=y−42=z−51
intersect, then-
If the lines x−21=y−31=z−4λ and x−1λ=y−42=z−51 intersect, then-
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Solution
The correct options are
A λ=−1
D λ=0
We know for two lines to intersect,
∣∣
∣∣x2−x1y2−y1z2−z1a1b1c1a2b2c2∣∣
∣∣=0
⇒∣∣
∣∣−11111λλ21∣∣
∣∣=0⇒−1(1−2λ)−1(1−λ2)+1(2−λ)=0
⇒λ2+λ=0⇒λ=0,−1
A λ=−1
D λ=0
We know for two lines to intersect,
∣∣ ∣∣x2−x1y2−y1z2−z1a1b1c1a2b2c2∣∣ ∣∣=0
⇒∣∣ ∣∣−11111λλ21∣∣ ∣∣=0⇒−1(1−2λ)−1(1−λ2)+1(2−λ)=0
⇒λ2+λ=0⇒λ=0,−1
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