Determine whether the vectors ( mathbf{A} = [1, 2, 3] ) and ( mathbf{B} = [4, -2, 0] ) are orthogonal.

Question

Accepted Answer

Step:1 ：Calculate the dot product of vectors ( mathbf{A} ) and ( mathbf{B} ). The dot product is defined as ( mathbf{A} cdot mathbf{B} = sum_{i=1}^{n} a_i b_i ), where ( a_i ) and ( b_i ) are the components of ( mathbf{A} ) and ( mathbf{B} ) respectively.Step:2 ：Substitute the given values into the dot product formula: ( mathbf{A} cdot mathbf{B} = (1)(4) + (2)(-2) + (3)(0) = 4 - 4 + 0 ).Step:3 ：If the dot product of two vectors is 0, they are orthogonal. So, we check the result of our calculation.

Answer

Step: 1 ：Calculate the dot product of vectors ( mathbf{A} ) and ( mathbf{B} ). The dot product is defined as ( mathbf{A} cdot mathbf{B} = sum_{i=1}^{n} a_i b_i ), where ( a_i ) and ( b_i ) are the components of ( mathbf{A} ) and ( mathbf{B} ) respectively.Step: 2 ：Substitute the given values into the dot product formula: ( mathbf{A} cdot mathbf{B} = (1)(4) + (2)(-2) + (3)(0) = 4 - 4 + 0 ).Step: 3 ：If the dot product of two vectors is 0, they are orthogonal. So, we check the result of our calculation.

Determine whether the vectors \( \mathbf{A} = [1, 2, 3] \) and \( \mathbf{B} = [4, -2, 0] \) are orthogonal.

Answer

Popular Problems