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Hmm I didnt understand how you found the unit vector OD. Isn't the length of i just OA = 14?OD = 4i+4j+5k
Now why? Well, start with 4i, this is because the length OA is 14m, and DE is 6, you need to subtract 6 from 14 and then divide by two, as this is how you'll get the length of i... Think about it, because I don't know how else to explain it. 4j because it goes halfway through the 8m, as the opposite side of the base rectangle are equal, so 8/2 = 4... so 4j. 5k is easy because they said the roof is at a height of 5cm, and k is the movement on the y axis, so 5k... 4i+4j+5k.
OB is much easier..
OB = 14i + 8j
14i because it moves 14m along from O to A, and then 8j because it moves 8m from A to B.
Now to find the angle...
a.b=|a||b|cosθ
4(14)+4(8) = √(4^2 + 4^2 + 5^2)√(14^2 + 8^2)cosθ
88 = √57 √260 cosθ
88=121.7cosθ
cosθ = 88/121.7
θ = cos^-1(88/121.7)
θ=43.7
... Yup correct![]()
I'll really appreciate if you could explain that to me from the diagram, that is, if you're free and don't mind to do so
The rest is all clear..