Question #180999

A plane travels passing coordinate (2,-1,-3) and (4,2,7). At the time of travel, wind

blows in parallel associating to the vector of .i+4j2k.i+ 4j- 2k. Describe the situation

according to the suitable mathematical concepts.

<10 marks>


1
Expert's answer
2021-04-15T07:34:04-0400



Points are

(2,-1,-3) , (4,2,7)



(4-2)i + (2+1)j + (7+3)k


a = 2i+3j+10k2i + 3j + 10k

This is vector equation



Wind - vector equation

b=i+4j2kb = i+ 4j- 2k


And

We know


a.b=abcos(θ)a.b = |a||b|cos(\theta)


cos(θ)=a.babcos(\theta) = {a.b \over |a||b|}


cos(θ)=611321cos(\theta) = { -6\over \sqrt {113} \sqrt{21}}


The angle between the plane direction and the wind direction

(θ)=cos1(611321)\boxed{(\theta) = cos^{-1}({ -6\over \sqrt {113} \sqrt{21}})}


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