Dot Product

Question

The value of (2î + 3ĵ) · (4î - 5ĵ) is

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1. **Component Method**: For vectors in 2D, $\vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2$.
2. **Substitution**:
   - $x$-components: $2 	imes 4 = 8$.
   - $y$-components: $3 	imes (-5) = -15$.
3. **Summation**:
   - $8 + (-15) = -7$.
4. **Note**: Since $\vec{a} \cdot \vec{b} < 0$, the angle between these vectors is obtuse.

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The dot product of vectors $a$ and $b$ is defined as