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

Step-by-step solution

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