1.u=<1,3,-2>; v=<-5,3,2>
The vectors are
u = i + 3j - 2k
v = -5i +3j + 2k
cosθ = ∣u∣∣v∣u.v
cosθ = 14∗38(i+3j−2k).(−5i+3j+2k)
cosθ = -14∗38−5+9−4 = 0
θ = 2π
Hence the vectors u and v are orthogonal to each other.
2.u=<1,-2,4>; v=<5,3,7>
The vectors are
u = i - 2j + 4k
v = 5i +3j + 7k
cosθ = ∣u∣∣v∣u.v
cosθ = 21∗83(i−2j+4k).(5i+3j+7k)
cosθ = 21∗835−6+28
cosθ = 21∗8327
cosθ = 0.647
θ = 49.68°
Since, θ < 90° so u and v make the acute angle with each other.
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