Consider a line passing through the point P ( 3 , 4 , 5 ) & having direction ratios ( 2 , − 2 , 1 ) . If image of point Q ( 1 , − 1 , 8 ) w.r.t. given line is Q ′ , then length of median of Δ PQQ ′ th

Question

Consider a line passing through the point P ( 3 , 4 , 5 ) & having direction ratios ( 2 , − 2 , 1 ) . If image of point Q ( 1 , − 1 , 8 ) w.r.t. given line is Q ′ , then length of median of Δ PQQ ′ through vertex P is - P ( 3 , 4 , 5 ) ( 2 , − 2 , 1 ) Q ( 1 , − 1 , 8 ) Q ′ △ PQQ ′

TestHub · Accepted Answer

Δ PQQ ′ is an isosceles triangle \& PM = 2 i ^ − 2 j ^ ​ + k ^ Now, PM = ∣ PQ ​ ∣ cos θ , ∣ PQ ​ ∣ = 2 i ^ + 5 j ^ ​ − 3 k ^ PM = ​ PM PQ ​ ⋅ PM ​ ​ = ​ 3 4 − 10 − 3 ​ ​ = 3

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