1. ## [SOLVED] vectors' coefficients

(these are 3d vectors that were in columnar form, but i posted in component form cuz i dont know how to type column form.)

(p[ 1i + 2j + 3k ] ) + (q[ 0i + 4j - 2k]) + (r[0i + 1j +2k]) = [1i + 0j + 1k]

find the values of the scalar quantities p, q, & r.

This may be upper-level math, but im a high schooler in IB math. i would appreciate somethin i could eazily follow...thx

2. Don't panic, this is a linear combiantion of vector.

Write the vectors in column and you will see that you have :

All the first entries of the vectors to the left must equal one,

$\displaystyle 1p+0q+0r =1$

All the second entries of the vectors to left must equal 0,

$\displaystyle 2p+4q+1r =0$

All the third entries of the vectors to the left must equal 1,

$\displaystyle 3p+2q+2r=1$

You are left with a system of linear equations as follow:

$\displaystyle p =1$
$\displaystyle 2+4q+r=0$
$\displaystyle 3+2q+2r=1$

I hope that you can finish this, you have two equations and two unknowns because you know that p =1 from the first equation.

Cheers