Dot Product

Identify Angle: Perpendicular vectors have an angle $θ = 9 0^{\circ}$ .
Apply Formula: $a \cdot b = ∣ a ∣∣ b ∣ cos 9 0^{\circ}$ .
Trigonometric Property: $cos 9 0^{\circ} = 0$ .
Result: $P ro d u c t = ∣ a ∣∣ b ∣ \cdot (0) = 0$ . This is the 'Orthogonality Condition'.

This easy 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