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Position Vectors

Example 2

Example 2 — Continued

Given points \(A~(1,-4)\) and \(B~(3,-1)\), find the position vector \(\overrightarrow{AB}\).

Solution

Draw OA and OB. Thus AB=-OA+OB.

Check Your Understanding B

Given the following vectors:

a → = ((s)*(a))*1.0 ((v)*(a))*1.0 ((s)*(a))*2.0 ((v)*(a))*2.0 ((s)*(a))*3.0 ((v)*(a))*3.0   

b → = ((s)*(b))*1.0 ((v)*(b))*1.0 ((s)*(b))*2.0 ((v)*(b))*2.0 ((s)*(b))*3.0 ((v)*(b))*3.0

 

Calculate | (s)*(a)(v)*(a) (d)*(a) → (s)*(b) (v)*(b) (d)*(b) → |

 

Enter an exact answer, e.g. 10 , 13 , 2 5 .

(Note: Use sqrt(z)  for z . Alternately, click on the Sigma symbol for Equation Editor icon to access the Equation Editor.)

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To calculate the given magnitude, we begin by simplifying (s)*(a)(v)*(a)(d)*(a)→(s)*(b)(v)*(b)(d)*(b)→, which becomes:

(((((c)*(o))*(e))*(f))*(f))*(a)(a)*1.0+(((((c)*(o))*(e))*(f))*(f))*(b)(b)*1.0,(((((c)*(o))*(e))*(f))*(f))*(a)(a)*2.0+(((((c)*(o))*(e))*(f))*(f))*(b)(b)*2.0,(((((c)*(o))*(e))*(f))*(f))*(a)(a)*3.0+(((((c)*(o))*(e))*(f))*(f))*(b)(b)*3.0=((d)*1.0,(d)*2.0,(d)*3.0)

 

We then evaluate the magnitude of this resulting vector:

|(s)*(a)(v)*(a)(d)*(a)→(s)*(b)(v)*(b)(d)*(b)→|=(d)*1.0,(d)*2.0,(d)*3.0=(d)*1.02+(d)*2.02+(d)*3.02=((((a)*(n))*(s))*(m))*(l)

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