In this page, you will learn about removing the direction of the vector cross product with an example application.

*click on the content to continue..*

An object by position vector `vec p` is at a distance from a screen. The screen is given by unit vector `vec s` Is the distance of the object from the screen a vector or scalar?

- a vector
- a vector
- a scalar

The answer is 'a vector'. The distance is a vector that terminates at the object and at `90^@` angle to the screen.

Note: In physics - Kinematics, distance and displacement are defined as scalar and vector. In coordinate geometry, distance from an object to another is a vector.

Given `vec p` and the screen `hat s`. what is the magnitude of distance of object from the screen?

- `|vec p xx hat s|`
- `|p| sin theta`
- both the above
- both the above

The answer is 'Both the above'.

An object by position vector `vec p` is at a distance from a screen. The screen is given by unit vector `vec s` We saw that the distance is a vector and the length of the distance is `|vec p xx hat s|`. What is the direction of the distance vector?

- unit vector along `vec p - (vec p cdot hat s) hat s`
- unit vector along `vec p - (vec p cdot hat s) hat s`
- Direction cannot be found

The answer is 'unit vector along `vec p - (vec p cdot hat s) hat s`'.

Vector cross product, by definition, is a vector. Depending on the application requirement, the direction can be removed.

** Distance using Cross Product: ** For a vector `vec p` and a direction given by unit vector `hat s`, the magnitude of distance of point given by `vec p` to the direction `hat s` is `|vec p xx hat s|`.

*slide-show version coming soon*