Answer to Question #180999 in Geometry for hinoki

Question

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 .$i+ 4j- 2k.$ Describe the situation

according to the suitable mathematical concepts.

<10 marks>

Answer 1

Points are

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

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

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

This is vector equation

Wind - vector equation

$b = i+ 4j- 2k$

And

We know

$a.b = |a||b|cos(\theta)$

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

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

The angle between the plane direction and the wind direction

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