Answer:
Check below
Step-by-step explanation:
Vectors are quantities that possess both magnitude and direction. In engineering problems, it is best to think of vectors as arrows, and usually it is best to manipulate vectors using components. In this tutorial, we consider the addition of two vectors using both of these techniques. Consider two vectors [tex]\vec{A}[/tex]and [tex]\vec{B}[/tex] that have lengths A and B, respectively. Vector [tex]\vec{B}[/tex] makes an angle?
1) Vector [tex]\vec{B}[/tex] makes an angle?
Yes, it does. Vector [tex]\vec{B}[/tex] makes an angle with [tex]\vec{A}[/tex], since both have the same origin and different direction.
2) From the direction of A.(Figure 1)In vector notation, the sum is represented by [tex]\vec{C}=\vec{A}+\vec{B}[/tex] where [tex]\vec{C}[/tex] is a new vector that is the sum of [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]. Find C, the length of C, which is the sum of A and B.
C is the resultant vector of this sum of vectors([tex](\vec{C}=\vec{A}+\vec{B})[/tex]
The length of c is found through the law of cosines, after projecting, vector a.
(Check 3rd picture)
2.2) The other technique to add vectors is to write them. As C is the resultant vector then we have
[tex]\vec{A}=\left \langle a_{1},a_{2} \right \rangle \vec{B}=\left \langle b_{1},b_{2} \right \rangle \vec{C}=\left \langle a_{1}+b_{1}, a_{2}+b_{2}\right \rangle[/tex]
