March 10, 2023
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 Ax1 + By1 + Cz1 + D / √(A2 + B2 + C2)
Now, let us substitute the given values into the formula, finding the distance from the origin:
2(0) - 3(0 + 6(0) +21) / √(22 + 32 + 62)
= 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!