If a = i + j + k , b = j - k then a vector c such that a c = b and a c =3 is

Step-by-step solution

Finding vector c from given conditions: Let c = x i + y j + z k . Given a = i + j + k and b = j - k , with a c = 3 and a c = b . The dot product yields a c = x + y + z = 3 . The cross product a c evaluates to (z - y) i - (z - x) j + (y - x) k , which equals b = 0 i + 1 j - 1 k . Component comparison gives z = y , x - z = 1 , and y - x = -1 . Substituting y = z into the dot product: x + 2z = 3 . With x - z = 1 , subtracting yields 3z = 2 , so z = 2 3 and x = 5 3 . Since y = z , y = 2 3 . Thus, c = 5 3 i + 2 3 j + 2