( a i )( a i )+( a j )( a j )+( a k )( a k ) is equal to

Step-by-step solution

Let a =a₁ i +a₂ j +a₃ k Then, a i =a₁, a j =a₂, a k =a₃ a i =-a₂ k +a₃ j , a j =a₁ k -a₃ i and a k =-a₁ j +a₂ i aligned & ( a i )( a i )+( a j )( a j )+( a k )( a k ) & =a₁ (-a₂ k +a₃ j )+a₂ (a₁ k -a₃ i ) & +a₃ (-a₁ j +a₂ i ) aligned =0