If p2 + q2 + r2 = 1 what is the value of (ar-pq)×(ap-qr)×(aq-pr)??
Explanation:
Given, (ar-pq)×(ap-qr)×(aq-pr)
Let’s consider ar-pq.
⇒ ar-pq = ar-1pq = a-rpq …(1)
Similarly,
ap-qr = a-pqr …(2)
aq-rp = a-qrp …(3)
Multiplying all three equation,
(ar-pq)×(ap-qr)×(aq-pr) = a-rpq×a-pqr×a-qrp
= a-rpq×a-pqr×a-qrp
= a-r2+p2+q2pqr
= a-1pqr [p2 + q2 + r2 = 1]
Hence, option (d).
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