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Bogdan [553]
3 years ago
10

Find the angle between (u= sqrt 5i) -8j and (v= sqrt 5i) +j. Round to the nearnest tenth of a degree.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
4 0

Answer:

68.9°

Step-by-step explanation:

u = √5i - 8j; v = √5i + j

lul = √(√5)² + (-8)² = √5 + 64 = √69

lvl = √(√5)² + 1 = √5 + 1 = √6

Let the angle be α

Hence, sin²α = (u X v)²/(lul²*lvl²)

sin²α = [(√5i - 8j)(√5i + j)]²/(√69)²*(√6)²

= (5i - 7j√5i - 8j²)²/(69 X 6) = (25 + 245 + 64)/(414)

sin²α =  334/414

sin α = √334/√414 = 18.28/20.35 = 0.8983

∴ α = sin^-1(0.8983) = 68.9°

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