Question

Find the dot product of the vectors \[ (11\mathbf{i} + \mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} + \mathbf{j} + 11\mathbf{k}). \]

• A. 22
• B. 23
• C. 24
• D. 20

Hint:

When calculating the dot product, multiply corresponding components of the vectors and add the results together.

Answer 1

The Correct Option is B

The dot product of the vectors \( \mathbf{A} = 11\mathbf{i} + \mathbf{j} + \mathbf{k} \) and \( \mathbf{B} = \mathbf{i} + \mathbf{j} + 11\mathbf{k} \) is given by: \[ \mathbf{A} \cdot \mathbf{B} = (11 \times 1) + (1 \times 1) + (1 \times 11) = 11 + 1 + 11 = 23. \] Thus, the correct answer is option (B) 23.