Let u→ be a vector on rectangular coordinate system with sloping angle 60o' Suppose that |u→−i^|  is geometric mean of |u→| and |u→−2i^|, where i^ is the unit vector along the x-axis. Then find the value is (2+1)|u→|

Since angle between u→ and i^ is 60∘ we haveu→⋅i=|u→||i^|cos⁡60∘=|u→|2Given that |u→−i^|,|u→|,|u→−2i^| are in G.P., so |u→−i^|2=|u→||u→−2i^|Squaring both sides|u→|2+|i^|2−2u→⋅i^2=|u→|2|u→|2+4|i^|2−4u→⋅i^ |u→|2+1−2|u→|22=|u→|2|u→|2+4−4|u→|2 or  |u→|2+2|u→|−1=0⇒|u→|=−2±222or  |u→|=2−1