Answer:

no

Explanation:

No, it is not necessary that vector B is perpendicular to vector C if vector A is perpendicular to both B and C.

Let vector A be along the x-axis, vector B along the y-axis, and vector C along the z-axis in three-dimensional space.

Vector A is perpendicular to both B and C because it lies in the x-y plane, and the x-y plane is perpendicular to both the y-axis (B) and the z-axis (C)

However, vector B (along the y-axis) and vector C (along the z-axis) are not perpendicular to each other. They are actually parallel to each other and lie in the y-z plane.

In this case, vector A is perpendicular to both B and C, but B is not perpendicular to C. Therefore, the perpendicularity of vector A with vectors B and C does not necessarily imply that B is perpendicular to C.

Verified answer

Answer:

No, it's not necessary

See attachment....

In 1st figure A is perpendicular to both but B is not perpendicular to C

And 2nd figure, where all perpendicularly placed just like xyz axis