KEAM 2011 Math Paper

since, the vector 8i+aj in the direction of the vector 4i−3j. That means both vectors are parallel to each other.
By condition of parallel vectors,
‌

8

4

=‌

a

−3

⇒a=−6
Alternative Method
Given also, ‌‌|8i+aj|=10
⇒‌‌√64+a2=10
⇒‌‌64+a2=100
⇒‌‌a2=36
⇒‌‌a=±6    (here we take (-) ve sign)
⇒‌‌a=−6