If b and c are any two non-collinear unit vectors and a is any vector, then ( a b ) b +( a c )+ a b c | b c | ( b c ) is equal to

Step-by-step solution

Let b = j and c = j | b c |=| k |=1 Again, let a =a₁ i +a₂ j +a₃ j Now, a b = a i = a ₁, b c = a k = a ₂ and a b c | b c | = a k = a ₃ aligned & ( a b ) b +( a c ) c + a ( b c ) | b c | ( b c ) & =a₁ b +a₂ c +a₃( b c )=a₁ i +a₂ j +a₃ k = a aligned