Meaning of the statement

The statement "The components of a vector along its perpendicular direction is always zero" means that when a vector is projected onto a line that is perpendicular to it, the component of the vector in that direction will always be zero.

Explanation

When a vector is projected onto a perpendicular line, the resulting vector is the projection of the original vector onto that line. The projection of the vector will be a scalar quantity that represents the component of the vector in the direction of the perpendicular line.

If the vector is projected onto a line that is perpendicular to it, the projection will be zero because there is no component of the vector in that direction. This is because the perpendicular line is orthogonal to the vector, and any component of the vector in that direction will be cancelled out by the direction of the perpendicular line.

For example, consider a vector that is pointing in the x-direction. If we project this vector onto the y-axis, the resulting vector will have a magnitude of zero because there is no component of the vector in the y-direction.

Similarly, if we project a vector onto a plane that is perpendicular to it, the resulting vector will have no component in the direction of the perpendicular plane.

Conclusion

In conclusion, the statement "The components of a vector along its perpendicular direction is always zero" means that when a vector is projected onto a line or plane that is perpendicular to it, the resulting vector will have no component in the direction of the perpendicular line or plane. This is because the perpendicular direction is orthogonal to the vector, and any component in that direction will be cancelled out.

Imagine a horizontal component perpendicular to the vectical that mean the value for horizontal becomes zero because the vertical component is maximum .... example the electric field is always perpendicular to the surface of a conductor that means the horizontal component of a electric field of a conductor is zero