Let a → = 1 ,   1 ,   − 1 , b → = 5 ,   − 3 ,   − 3 and c → = 3 ,   − 1 ,   2 . If r → is collinear with c → and has length of a → + b → 2 , then r → equals

Step-by-step solution

Since r → is collinear with c → , we can write, r → = k c → r → = k c → Given, r → = a → + b → 2 ∴ a → + b → 2 = k c → 6 i ^ − 2 j ^ − 4 k ^ = 2 k 3 i ^ − j ^ + 2 k ^ 56 = 2 k 14 ∴ k = ± 1 ∴ r → = ± c →