Vector Long Questions (Question 2)


Question 2:
Given that   AB =( 10 14 ),  OB =( 4 6 ) and   CD =( m 7 ) , find
(a) the coordinates of A,
(b) the unit vector in the direction of   OA .
(c) the value of m if CD is parallel to AB .

Solution:
(a)
AB = AO + OB ( 10 14 )=( x y )+( 4 6 ) ( x y )=( 10 14 )( 4 6 ) AO =( 6 8 ) OA =( 6 8 ) A=( 6,8 )
(b)
| OA |= ( 6 ) 2 + ( 8 ) 2 | OA |= 100 =10 the unit vector in the direction of  OA = OA | OA | = ( 6 8 ) 10 = 1 10 ( 6 8 ) =( 3 5 4 5 )
(c)
Given  CD  parallel  AB   CD =k AB ( m 7 )=k( 10 14 ) ( m 7 )=( 10k 14k ) 7=14k k= 1 2 m=10k=10( 1 2 )=5