Question

Tolong bantuannya~
sekaligus cara kerjanya

Answer 1

OA = a = (t^2 + 1, t)
OB = b = (1, 2) => |b| = √(1^2 + 2^2) = √(1 + 4) = √5

OA.OB = (t^2 + 1)(1) + t(2) = t^2 + 2t + 1

Panjang proyeksi OA terhadap OB < 9/√5
(OA.OB) / |OB| < 9/√5
(t^2 + 2t + 1)/√5 < 9/√5
t^2 + 2t + 1 < 9
t^2 + 2t - 8 < 0
(t + 4)(t - 2) < 0
t = -4 atau t = 2
Garis bilangan
+++ (-4) --- (2) +++
-4 < t < 2

Answer 2

|OB| = √(1^2 + 2^2) = √(1 + 4) = √5

OA.OB = (t^2 + 1)(1) + t(2) = t^2 + 2t + 1

Panjang proyeksi OA terhadap OB < 9/√5
(OA.OB) / |OB| ≤ 9/√5
(t^2 + 1 ,t) (1,2) /√5 ≤ 9/√5
(t^2 + 1)(1) + t(2) /√5 ≤ 9/√5
[√5 dicoret]

t^2 + 2t + 1 ≤ 9
t^2 + 2t + 1 - 9 ≤ 0
t^2 + 2t - 8 ≤ 0
(t + 4)(t - 2) ≤ 0
t = -4 ≤ 0 atau
0 ≤ t = 2

-4 ≤ t ≤ 2 ( E )