First slide

Application of vectors in geometry

Question

If the vector product of a constant vector $\vec{O A}$ with a variable vector $\vec{O B}$ in a fixed plane OAB be a constant vector, then the locus of B is

Moderate

A

a straight line perpendicular to $\vec{O A}$
B

a circle with centre o and radius equal to $\vec{O A}$
C

a straight line parallel $\vec{O A}$
D

none of these

Solution

$| \vec{a} \times \vec{r} | = | \vec{c} |$
Triangles on the same base and between the same parallel will have the same area.

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