Answer :

Let OA be the line joining the origin (0,0,0) and the point A(2,1,1).

Let BC be the line joining the points B(3,5,−1) and C(4,3,−1)


Direction ratios of OA = (a1, b1, c1) ≡ [(2 - 0), (1 - 0), (1 - 0)] ≡ (2,1,1)


Direction ratios of BC = (a2, b2, c2) ≡ [(4 - 3), (3 - 5), (-1 + 1)]


≡ (1, -2, 0)


Given-


OA is to BC


we have to prove that -


a1a2 + b1b2 + c1c2 = 0


L.H.S = a1a2 + b1b2 + c1c2 = 2 × 1 + 1 × (−2) + 1 × 0 = 2 - 2 = 0


R.H.S = 0


Thus, L.H.S = R.H.S ….PROVED


Hence OA is to BC.


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