Question

If vector u has its initial point at (-7, 3) and its terminal point at (5,-6), u= ? i + ? j. If v= -11i + 3j, 2u -v = ? i+? j.

Answer 1

a)
`\vec u = 12i -9j`, b)
`\vec r = 35i -21j`

Explanation:

a) The vector u is:

`\vec u = [5-(-7)]i + [(-6)-3]j`

`\vec u = 12i -9j`

b) The resultant vector is:

`\vec r = 2\vec u - \vec v`

`\vec r = 2\cdot (12i -9j)-(-11i+3j)`

`\vec r = (24+11)i+ (-18-3)j`

`\vec r = 35i -21j`

Answer 2

(a)

u = 12i - 9j

(b)

35i - 21j

Explanation:

Since the terminal point is (5,-6) and the initial point is (-7,3) then

u = (5,-6) - (-7,3) = (5- (-7) , -6 - 3 ) = ( 12 , -9 )

And you can write it in terms of i,j as follows

u = 12i - 9j

Then

2u - v = 24i - 18j +11i - 3j = 35i - 21j