Calculate projection of b on to the plane spanned by a1 and a2

Question: Calculate p = x1a1+x2a2, the projection of b onto the plane spanned by a1 and a2.

Given: a1 = [1; 2; -4] ; a2 = [2; 5; 3] ; b = [0; 1; 4]

I am trying to figure out how to solve this question in MATLAB. I am new to MATLAB and learning how to use this software. I tried to brainstorm a lot on this question but I cannot figure out how to solve this. Please, can you help me solve this question? Your help will be appreciated. Thank you.

[John D'Errico]

I think you need to write down the mathematics. Once you do, writing it in MATLAB will be trivial. But if you don't understand the mathematics, you are lost. So time to start writing, maybe some reading. What do you know about this? To start with, what is the equation of a plane? (Note that I WON'T do this for you. But I WILL guide you to the solution, IF you make an effort. If all else fails, try Google. It is your friend.)

[John D'Errico]

I'm still waiting. How do you define a plane? Surely you can find the equation of a plane somewhere.

[Roger Stafford]

Like John, I will not solve the problem for you, but here is a hint to get you going. Write an expression for the square of the distance between the point b and the point p as a function of coefficients x1 and x2. What you are seeking is the pair of values for x1 and x2 that minimizes this quantity. Now how could you derive the solution to a problem like that?