Answer to Question #127042 in Algebra for Ashley

Question

Given that A=−(5,−1) and B=(2,6) and the following statements: (i) AB–––– and BA–––– have the same directions; (ii) BA––––=−(7,5); (iii) AB–––– and BA–––– have different magnitudes; (iv) BA––––=−AB––––. Which one of the following is true?
A. Only (ii) and (iv) are true.
B. (i), (ii), (iii) and (iv) are all true.
C. Only (ii) is true.
D. Only (i) is true.

Answer 1

Option A is the answer

(ii) BA = -(7,5)

BA. = -(5,-1). - (2,6 )

=. (-5 -2 , 1-6)

= (-7,-5)

=. -(7,5 ). Hence it's true

(iv ) BA = - AB

-(7,5) = -{ (2,6 ) - ( -(5 ,-1)

=. -{ (2,6 ) - (-5,1)

=. -{2 +5. , 6-1}

=. -{ 7 ,5 } hence it's true.