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Grade: upto college level
        If A ⃗,B ⃗,C ⃗ are mutually perpendicular, show that C ⃗×(A ⃗×B ⃗) = 0. Is the converse true ?
5 years ago

Answers : (1)

Navjyot Kalra
askIITians Faculty
654 Points
							16. Given that A ⃗  B ⃗ and C ⃗ are mutually perpendicular 
A ⃗  × B ⃗. is a vector which direction is perpendicular to the plane containing A ⃗
Also C ⃗ is perpendicular to A ⃗ and B ⃗
∴ Angle between C ⃗ and A ⃗ x B ⃗ is 0° or 180° (fig. 1)
So, C ⃗ x (A ⃗ x B ⃗) = 0
The Converse is not true.
For example, if two of the vector are parallel, (fig. 2), then also
C ⃗ x (A ⃗ x B ⃗) = 0
So, they need not be mutually perpendicular.

						
5 years ago
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