vector in 2d dimensional space

1)vs = k vq + vrvs * vp = k vq * vp + vr * vp0 = 5k - 4 ...... vs and vp are orthogonal so vs * vp = 0k = 4/5

2)va - vb is perpendicular to 2va + vb :
(va - vb) (2va + vb) = 0
2(va)² - va * vb - (vb)² = 0 ... (1)
8va - 5vb is perpendicular to va + vb :
(8va - 5vb) (va + vb) = 0
8(va)² + 3va * vb - 5(vb)² = 0 ... (2)
(1) * 3 + (2) :

14(va)² - 8(vb)² = 0
(va)² : (vb)² = 4 : 7
|va|² cos0 : |vb|² cos0 = 4 : 7
|va| : |vb| = 2 : √7