Q6.5: NCERT Physics - Part 1 SYSTEMS OF PARTICLES AND ROTATIONAL MOTION 6.5 Solution: Show that a.(b _ c) is equal in magnitude to the volume of the…

Question

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Show that a.(b _ c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors a, b and c.

Accepted Answer

**Answer:**

|\vec{a} \cdot (\vec{b} \times \vec{c})| = \text{Volume}

**Step-by-Step Explanation:** The volume of a parallelepiped with sides

\vec{a}

,

\vec{b}

,

\vec{c}

is:

V = \text{base area} \times \text{height} = |\vec{b} \times \vec{c}| \times |\vec{a}| |\cos\theta| = |\vec{a} \cdot (\vec{b} \times \vec{c})|

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Step-by-Step Verified Solution