If a = i ^ − j ^ + k ^ and b = 2 i ^ + 4 j ^ + 3 k ^ are one of the sides and medians respectively, of a triangle through the same vertex, then area of triangle is-

Question

If a = i ^ − j ^ ​ + k ^ and b = 2 i ^ + 4 j ^ ​ + 3 k ^ are one of the sides and medians respectively, of a triangle through the same vertex, then area of triangle is-

TestHub · Accepted Answer

​ a = i ^ − j ^ ​ + k ^ ​ b = 2 i ^ + 4 j ^ ​ + 3 k ^ ​ b = 2 a + c ​ ​ ​ ∴ Area = 2 1 ​ ∣ a × c ∣ ​ = 2 1 ​ ∣ a × ( 2 b − a ) ∣ ​ = ∣ a × b ∣ − = ​ i ^ ​ j ^ ​ ​ k ^ 1 ​ − 1 ​ 12 ​ 4 ​ 3 ​ ​ = 86 ​

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