Equation Of The Ascent Path Of An Airplane

Equation Of The Ascent Path Of An Airplane
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The ascent path of an airplane is a straight line going through points A and B. The radius vectors of A and B are a and b respectively with respect to some origin.
Determine the equation of the ascent path of the airplane.

The strings: S₇P₄A₄₁ (motion-linear).

The math:
Pj Problem of Interest is of type motion (linear).

Equation Of The Ascent Path Of An Airplane

Consider figure 7.7, Let point P with radius vector r with respect to the same origin be on the ascent path of the airplane.
Then vectors r - a and b - a are parallel
So, r - a = λ(b - a)
Where λ is a parameter.
So, equation of ascent path is of the form :
r = a + λ(b - a)-------(1)
Equation (1) can be expressed as a vector (cross) product:
(r - a) x (b - a) = 0.

Math

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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