Question

a particle in equilibrium under the action of three vectors acting simultaneously . prove : vectorA× vectorB=vectorB×vectorC=vector C×VectorA​

Answer 1

Explanation:

An algebraic argument: start with the given information:- −A+B+C=0.

cross with one of the vectors, sayA. Note that A×A=0.

Note that B×A=−A×B.

conclude that A×B=C×A.

Similarly for the other equations.

A geometric argument:- The three vectors are the sides of a triangle in order. The area of the triangle is half the cross product of two of them in that order.

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