**I/GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Algebra**

**Exam Question:**

Find the length of the perpendicular drawn from the origin to the plane 2x − 3y + 6z + 21 = 0.

**Answer:**

For I/GCSE Mathematics, you should know:

We are given the equation 2x - 3y + 6z + 21 = 0, from the equation you have learnt; **Ax + By + Cz + D = 0**.

The equation can be **re-written** as Ax_{1} + By_{1} + Cz_{1 }+ D / √(A^{2} + B^{2} + C^{2})

Now, let us **substitute the given values** into the formula, finding the distance from the origin:

2(0) - 3(0 + 6(0) +21) / √(2^{2} + 3^{2} + 6^{2})

= 21 / √(49)

= 21 / 7

= **3**

As a result, we can find that the length of the perpendicular is 2x - 3y + 6z + 21 = 0 is **3 units**.

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!