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Question

If l21+m21+n21=1,etc and l1l2+m1m2+n1n2=0 and
Δ=∣ ∣l1m1n1l2m2n2l3m3n3∣ ∣ then

A
|Δ|=3
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B
|Δ|=2
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C
|Δ|=1
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D
|Δ|=0
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Solution

The correct option is C |Δ|=1
We have
Δ2=ΔΔ=∣ ∣l1m1n1l2m2n2l3m3n3∣ ∣∣ ∣l1m1n1l2m2n2l3m3n3∣ ∣
Δ2=ΔΔ=∣ ∣ ∣l21+m21+n21l1l2+m1m2+n1n2l1l3+m1m3+n1n3l1l2+m1m2+n1n2l22+m22+n22l2l3+m2m3+n2n3l1l3+m1m3+n1n3l2l3+m2m3+n2n3l23+m23+n23∣ ∣ ∣
=∣ ∣100010001∣ ∣=1Δ=±1|Δ|=1

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