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How is the magnitude of the scalar triple product is the volume of a parallelopiped formed by adjacent sides given by the three vectors a , b and c . (The bold letters represent vectors)

How is the magnitude of the scalar triple product is the volume of a parallelopiped formed by adjacent sides given by the three vectors a, b and c.
(The bold letters represent vectors)

Grade:12

2 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
6 years ago
Hi,

When you do AxB, it represents the area of a parallelogram, i.e. a two dimensional figure.
But when we take its dot product with the third vector , that means we are taking the component of height along the vector which is perpendicular to its area.

Which means its Volume. Because taking a perpendicular component with area is like fnding area of Cube.

So we first take cross to find area and than dot to find the component and thats how [ a b c] represents the volume.
Ankit Jaiswal
165 Points
5 years ago
When you do AxB, it represents the area of a parallelogram, i.e. a two dimensional figure.But when we take its dot product with the third vector , that means we are taking the component of height along the vector which is perpendicular to its area.Which means its Volume. Because taking a perpendicular component with area is like fnding area of Cube.So we first take cross to find area and than dot to find the component and thats how [ a b c] represents the volume.

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