Question

Find the dot product of the vectors \[ (7\mathbf{i} - 8\mathbf{j} + 9\mathbf{k}) \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}). \]

• A. 25
• B. 24
• C. 23
• D. 22

Hint:

To compute the dot product of two vectors, multiply the corresponding components and add the results.

Answer 1

The Correct Option is B

The dot product of two vectors \( \mathbf{A} = a_1\mathbf{i} + b_1\mathbf{j} + c_1\mathbf{k} \) and \( \mathbf{B} = a_2\mathbf{i} + b_2\mathbf{j} + c_2\mathbf{k} \) is given by: \[ \mathbf{A} \cdot \mathbf{B} = a_1a_2 + b_1b_2 + c_1c_2. \] For the vectors \( \mathbf{A} = 7\mathbf{i} - 8\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{B} = \mathbf{i} - \mathbf{j} + \mathbf{k} \), we calculate: \[ \mathbf{A} \cdot \mathbf{B} = 7 \times 1 + (-8) \times (-1) + 9 \times 1 = 7 + 8 + 9 = 24. \] Thus, the correct answer is option (B) 24.