Let a → = i ^ - j ^ , b → = j ^ - k ^ and c → = k ^ - i ^ . If d → is a unit vector such a → · d → = 0 = b → c → d → , then d → is

Step-by-step solution

Let d → = d 1 i ^ + d 2 j ^ + d 3 k ^ . Given a → ⋅ d → = 0 . ⇒ d 1 - d 2 = 0 ⇒ d 1 = d 2   . . . . . . . . . . . i Also, given d → is a unit vector. ⇒ d 1 2 + d 2 2 + d 3 2 = 1   . . . . . . . . . ii Also, given b → c → d → = 0 . ⇒ 0 1 - 1 - 1 0 1 d 1 d 2 d 3 = 0 ⇒ - 1 - d 3 - d 1 - 1 - d 2 = 0 ⇒ d 1 + d 2 + d 3 = 0 ⇒ 2 d 1 + d 3 = 0 (from equation i ) ⇒ d 3 = - 2 d 1   . . . . . . . . . . . iii Putting e