If b→ is a vector whose initial point divides the join of 5i^ and 5j^ in the ratio k:1  and whose terminal point is the origin and |b→|≤37 then k lies in the interval

The point that divides 5i^ and 5j^ in the ratio of k:1 is (5j^)k+(5i^)1k+1∴ b→=5i^+5kj^k+1 Also, |b→|≤37⇒ 1k+125+25k2≤37 or  51+k2≤37(k+1)Squaring both sides, we get 251+k2≤37k2+2k+1or  6k2+37k+6≥0 or (6k+1)(k+6)≥0k∈(−∞,−6]∪−16,∞