Question

Let 𝒖 = −2𝒊 + 𝒋, 𝒗 = 3𝒋 6a) Find (ai) 𝒖 + 𝒗 , (aii) 𝒖 − 𝒗, and (aiii) 2𝒖 − 3𝒗, Then sketch each resultant vector.?

Answer 1

See below.

Explanation:

`bbu=-2bbi+bbj`

`bbv=3bbj`

(ai)

`bbu+bbv=-2bbi+bbj+3bbj=-2bbi+4bbj \ \ \ \[ x]`

(aii)

`bbu-bbv=-2bbi+bbj-(3bbj)=-2bbi-2bbj \ \ \ \ \[y]`

(iii)

`2bbu-3bbv= 2(-2bbi+bbj)-3(3bbj)=-4bbi-7bbj \ \ \ \ \[z]`

I haven't plotted these all as position vectors in order to fit them in the same plot. All resultant vectors are in green.