Let a → = i ^ + 2 j ^ + 3 k ^ , b → = i ^ - j ^ + 2 k ^ and c → = x - 2 i ^ - x - 3 j ^ - k ^ . If c → lies in the plane of a → and b → , then 1 x is equal to

Question

Let a → = i ^ + 2 j ^ + 3 k ^ , b → = i ^ - j ^ + 2 k ^ and c → = x - 2 i ^ - x - 3 j ^ - k ^ . If c → lies in the plane of a → and b → , then 1 x is equal to,

MARKS App · Accepted Answer

c → , a → , b → are coplanar ⇒ a → b → c → = 0 1 2 3 1 - 1 2 x - 2 - x - 3 - 1 = 0 ⇒ 1 1 + 2 x - 6 - 2 - 1 - 2 x + 4 + 3 - x + 3 + x - 2 = 0 ⇒ 2 x - 5 - 6 + 4 x + 3 = 0 ⇒ 6 x - 8 = 0 ⇒ x = 4 3

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