[Solved] Prove that A.(A×B)=0. - Concepts of Physics

To prove:A.(A×B)=0Proof: Vector product is given by A×B=∣∣A∣∣∣∣B∣∣sinn^∣∣A∣∣∣∣B∣∣sinn^ is a vector which is perpendicular to the plane containing∣∣A∣∣∣∣B∣∣sinn^ 4This implies that it is also perpendicular to ∣∣A∣∣∣∣B∣∣sinn^. We know that the dot product of two perpendicular vectors is zero.∴ ∣∣A∣∣∣∣B∣∣sinn^Hence, proved.

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Prove that {A} . ( {A} {B} ) = 0.

Concepts of Physics

Class 11

HC Verma Part I

Chapter 1: Introduction to Physics

35 questions

Chapter 2: Physics and Mathematics

60 questions

Let

a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k

. Find the angle between them.

Prove that

A . (A \times B) = 0

A = 2 i + 3 j + 4 k and B = 4 i + 3 j + 2 k

find

A \times B

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Question

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Prove that $A . (A \times B) = 0$ .

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Concepts of Physics (HC Verma Part I)

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A . (A \times B) = 0

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Text solutionVerified

To prove:

A . (A \times B) = 0

Proof: Vector product is given by

A \times B = ∣ ∣ A ∣ ∣ ∣ ∣ B ∣ ∣ sin \overset{n}{^}

∣ ∣ A ∣ ∣ ∣ ∣ B ∣ ∣ sin \overset{n}{^}

is a vector which is perpendicular to the plane containing

∣ ∣ A ∣ ∣ ∣ ∣ B ∣ ∣ sin \overset{n}{^}

4
This implies that it is also perpendicular to

∣ ∣ A ∣ ∣ ∣ ∣ B ∣ ∣ sin \overset{n}{^}

. We know that the dot product of two perpendicular vectors is zero.∴

∣ ∣ A ∣ ∣ ∣ ∣ B ∣ ∣ sin \overset{n}{^}

Hence, proved.

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Question Text	Prove that $A . (A \times B) = 0$ .
Topic	Physical World
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	141

Prove that $A . (A \times B) = 0$ .

Text solutionVerified

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