Vector (i-j=k): Why Does MA=i+j+k?

[desmond iking]

Homework Statement

I can't understand why the vector MA finally become (i+j+k) ?? is it beacuse of (i-j ) becomes k ??

Homework Equations

The Attempt at a Solution

 

[ShayanJ]

That's wrong!
$(i-j)\times (i+j)=\underbrace{i\times i}_0+i \times j- j\times i-\underbrace{ j \times j}_0=i\times j+i\times j=2 i \times j=2 k$

 

[haruspex]

That's wrong!
$(i-j)\times (i+j)=\underbrace{i\times i}_0+i \times j- j\times i-\underbrace{ j \times j}_0=i\times j+i\times j=2 i \times j=2 k$

It's wrong before that, even.
$\vec P = P(\vec j -\vec k)/\sqrt 2$
Alternatively, by calculating the distance from A to the line of P the moment is seen to have magnitude $aP\sqrt {\frac 32}$. I believe the correct answer is exactly half that shown.

 

[Don Bari]

-j X i=k
That k and the other normal one from i x j=k, add up to 2k.