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Prove that A ⃗ ∙(A ⃗×B ⃗ )=0.

Prove that A ⃗ ∙(A ⃗×B ⃗ )=0.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
. A ⃗ (A ⃗ x B ⃗) = 0 (claim) As, A ⃗ x B ⃗ ABsin θ n ̂ AB sin θ n ̂ is a vector which is perpendicular to the plane containing A ⃗ and B ⃗ , this implies that it is also perpendicular to A ⃗ . As dot product of two perpendicular vector is zero.

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