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If A ⃗,B ⃗,C ⃗ are mutually perpendicular, show that C ⃗×(A ⃗×B ⃗) = 0. Is the converse true ?

If A ⃗,B ⃗,C ⃗ are mutually perpendicular, show that C ⃗×(A ⃗×B ⃗) = 0. Is the converse true ?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
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.

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