If b→ is a vector whose initial point divides the join of 5i^ and 5j^ in the ratio p:1 and whose terminal point is the origin and |b→|≤37 then p lies in the interval
[−6,−1/6]
(−∞,−6]∪[−1/6,∞)
[0, 6]
none of these
The point that divides 5i^ and 5j^ in the ratio of p:1 is (5j^)p+(5i^)1p+1∴ b→=5i^+5pj^p+1
Also, |b→|≤37
⇒ 1p+125+25p2≤37 or 51+p2≤37(p+1)
Squaring both sides, we get
251+p2≤37p2+2p+1or 6p2+37p+6≥0 or (6p+1)(p+6)≥0p∈(−∞,−6]∪−16,∞