diketahui tan β=8/15(β sudut antara vektor u dan v, β lancip). Jika panjang vektor |u|=17, panjang vektor |v|=4, hitunglah (vektor u-vektor v).2vektor u pliss j

#tan beta = 8/15 (tan = depan/samping)
cos alfa = 15/17 (rumus phytagoras)

cos a = u.v/|u|.|v|
15/17 = u.v/17.4
15/17 = u.v/68
15/17 × 68 = u.v
15.4 = u.v
60 = u.v

(u-v). 2u = 2u.u - 2u.v
= 2.|u|* - 2u.v
= 2(17)* - 2.60
= 2(289) - 120
= 578 - 120
= 458

Tan b = 8/15 = de/sa => mi = √(8^2 + 15^2) = √(64 + 225) = √289 = 17
Cos b = sa/mi = 15/17

(u - v) . 2u
= 2u.u - 2u.v
= 2|u|^2 - 2 |u|.|v| cos b
= 2(17)^2 - 2 . 17 . 4 . 15/17
= 2(289) - 8 . 15
= 578 - 120
= 458