Dot Product

Question

If two vectors are perpendicular, their dot product is

RankGuru · Accepted Answer

1. **Identify Angle**: Perpendicular vectors have an angle $	heta = 90^{\circ}$.
2. **Apply Formula**: $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 90^{\circ}$.
3. **Trigonometric Property**: $\cos 90^{\circ} = 0$.
4. **Result**: $Product = |\vec{a}| |\vec{b}| \cdot (0) = 0$. This is the 'Orthogonality Condition'.

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Dot Product

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Dot Product

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The value of (2î + 3ĵ) · (4î - 5ĵ) is

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