## Foot of Perpendicular is a** hot topic** for **H2 Prelims** and **A Levels**. It **comes out almost every year**.

There are two versions of Foot of Perpendicular, **from point to line**, and **from point to plane**. However, the two are highly similar, and the following article will teach how to **understand and remember** them.

## H2: Vectors (Foot of perpendicular)

From point (B) to Line ( )

(Picture)

### Equation (I):

Where does F lie? F lies on the line .

### Equation (II):

Perpendicular:

### Final Step

Substitute Equation (I) into Equation (II) and solve for .

## Example:

[CJC 2010 P1Q7iii]

Relative to the origin , the points , and have position vectors , and Find the shortest distance from to . Hence or otherwise, find the area of triangle .

[Note: There is a 2nd method to this question. (cross product method)]

## Solution:

Let the foot of perpendicular from C to AB be F.

Equation (I):

Equation (II):

Area of

For the next part, please read our article on Foot of Perpendicular (from point to plane).

## H2 Maths Tuition

If you are looking for Maths Tuition, contact Mr Wu at:

Email: mathtuition88@gmail.com