Two non-parallel vectors ( A ) and ( B ) are placed tail–to–tail at the origin of a…

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Two non-parallel vectors

\vec A

and

\vec B

are placed tail–to–tail at the origin of a rectangular coordinate system. (i) State the definition of the vector (cross) product of two vectors. (ii) Explain, with the aid of the right-hand rule, how the direction of

\vec A\times\vec B

is decided. Why does reversing the order of the vectors reverse the direction of the product? (iii) If

\vec A = 3\,\hat i

and

\vec B = 4\,\hat j

, write the unit vector directions of

\vec A\times\vec B

and

\vec B\times\vec A

. Hence comment on the relationship between the two results.

Related theory

Vector Operations
Vectors
Cross Product
Vector Algebra
Vector product
Cross product of two vectors

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