U and v are position vectors with terminal points at (6, 14) and (3, 7), respectively. Find the terminal point of 2u - v.

(-12, 0))
(0, 0)
(9, 21)
(15, 21)

The terminal point of 2u - v is (9 , 21) ⇒ 3rd answer

Step-by-step explanation:

The position vector is the vector whose starting point is the origin (0 , 0)

You can find it from its terminal point on it (a, b), the vector is <a - 0 , b - 0> = <a , b>

∵ u is a position vector with terminal point (6 , 14)

∴ u = <6 - 0 , 14 - 0>

∴ u = <6 , 14>

∵ v is a position vector with terminal point (3 , 7)

∴ v = <3 - 0 , 7 - 0>

∴ v = <3 , 7>

∵ 2u - v = 2<6 , 14> - <3 , 7>

- Multiply 6 and 14 by 2

∴ 2u - v = <12 , 28> - <3 , 7>

- Add subtract 3 from 12 and 7 from 28

∴ 2u - v = <9 , 21>

∴ The terminal point of 2u - v = (9 , 21)

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