If the four points, whose position vectors are 3 i ^ - 4 j ^ + 2 k ^ , i ^ + 2 j ^ - k ^ , - 2 i ^ - j ^ + 3 k ^ and 5 i ^ - 2 α j ^ + 4 k ^ are coplanar, then α is equal to

Question

If the four points, whose position vectors are 3 i ^ - 4 j ^ + 2 k ^ , i ^ + 2 j ^ - k ^ , - 2 i ^ - j ^ + 3 k ^ and 5 i ^ - 2 α j ^ + 4 k ^ are coplanar, then α is equal to, 73 17, - 107 17, - 73 17, 107 17

MARKS App · Accepted Answer

Let the four points be A : ( 3 , - 4 , 2 ) , B : ( 1 , 2 , - 1 ) , C : ( - 2 , - 1 , 3 ) and D : ( 5 , - 2 α , 4 ) A , B , C , D are coplanar points, then ⇒ 1 - 3 2 + 4 - 1 - 2 - 2 - 3 - 1 + 4 3 - 2 5 - 3 - 2 α + 4 4 - 2 = 0 ⇒ - 2 6 - 3 - 5 3 1 2 - 2 α + 4 2 = 0 ⇒ - 3 α + 146 = 0 ⇒ α = 73 17

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