Dot Product

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

This medium difficulty mathematics question is from the chapter vector algebra, covering the topic of dot product. It appeared in the 2025 exam.

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Dot Product

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Solution

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