Question

The following is an equation in physics (Newton's Law of Gravitation), in which G is a constant equal to 6.673e-11, and m1, m2, and r are all vectors of size n by 1 .  

How can this be calculated in matlab? and what is the array type of variable F ?

a.

F = G*m1.*m2./r^2;

F will be a scalar value.

b.

F = G*(m1.*m2)./r*r;

F will be a row array.

c.

F = G*m1.*m2./r.^2;

F will be a square matrix.

d.

F = G*m1.*m2./r.^2;

F will be a column vector.

e.

F = G*(m1.*m2) /r.*r;

F will be a scalar value.

Answer 1

Answer : Option(d) (F will be a column vector)

Explanation :

Given that m1,m2 and r are vectors of size n by 1 means m1,m2,r are column vectors.And G is a constant.So this will be calculated in matlab as follow.
G * m1 means multipling each element in m1 vector with G and there is .* operator and ./ operator in between m1,m2 and m2,r which means these operation are performed element by element.Example if 1,2,3 are elements in one vector and 4,5,6 are elements of another matrix then .* will multiply element by element(1*4,2*5,3*6) which results same vector size.So after performingn .* and ./ the result is still column matrix.And r^2 is just like G*m1 ,powers each elements by 2.So Finally the result F will be a column matrix.

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