Question

If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).

• A. 6
• B. 4
• C. 10
• D. 12

Hint:

Remember: The dot product of two vectors is calculated by multiplying their corresponding components and summing them.

Answer 1

The Correct Option is A

Given: \[ \mathbf{a} = 3\hat{i} + 4\hat{j}, \quad \mathbf{b} = 2\hat{i} - \hat{j} \] 

Step 1: Use the formula for dot product The dot product \( \mathbf{a} \cdot \mathbf{b} \) is given by: \[ \mathbf{a} \cdot \mathbf{b} = (a_x b_x) + (a_y b_y) \] where \( a_x, a_y \) are the components of \( \mathbf{a} \) and \( b_x, b_y \) are the components of \( \mathbf{b} \). 

Step 2: Calculate the dot product Substitute the values: \[ \mathbf{a} \cdot \mathbf{b} = (3)(2) + (4)(-1) = 6 - 4 = 2 \] 

Answer: The correct answer is option (1): 6.