Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

Prove that → a . ( → a × → B ) = 0 . - Physics

Prove that $\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0$.

Solution

To prove:

$\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0$

Proof: Vector product is given by $\vec{A} \times \vec{B} = \left| \vec{A} \right|\left| \vec{B} \right| \sin \hat {n}$

$\left| \vec{A} \right|\left| \vec{B} \right| \sin\hat { n }$

is a vector which is perpendicular to the plane containing

$\vec{A} \text { and } \vec{B}$ This implies that it is also perpendicular to $\vec{A}$. We know that the dot product of two perpendicular vectors is zero.

∴ $\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0$

Hence, proved.

Concept: What is Physics?
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 14 | Page 29
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