X = ap + bq + cr
{ 3 = a + 2c
{ -3 = b - c
{ 4 = 2a + b +4c
{ 6 = 2a + 4c
{ 4 = 2a + 4c + b
{ 3 = c - b
{b = -2
{c = 3 + b = 3 - 2 = 1
{a = 3 - 2c =3 - 2 = 1
X = p - 2q + r
10.
A = f*s = 4*5 + (-1)*3 + 1*(-2) = 20 - 3 - 2 = 15
11.
c = (x; y; z), y < 0
a = (0; 2; -1)
b = (-1; 2; -3)
ac = 2y - z = 0 => z = 2y
bc = -x + 2y - 3z = 0 => -x + 2y - 6y = 0 => x = -4y
c = (-4y; y; 2y)
|c| = √(16y² + y² + 4y²) = √(21y²) = √7
21y² = 7
y² = 1/3
y = -1/√3
c = (4/√3;-1/√3 ;-2/√3)