Answer:
Displacement = [tex]12\hat{i} +7\hat{j}[/tex]
Magnitude of displacement = 13.89 units
Angle of displacement = 30.26°
Explanation:
Mark the co-ordinates of each of the end points of the vectors.
The marked co-ordinates are shown below.
Displacement is the shortest distance between two points. Here, displacement between the starting and end points is the vector [tex]\overrightarrow{OA}[/tex].
Displacement vector for a point A[tex](x,y)[/tex] from origin O is given as:
[tex]\overrightarrow{OA}=(x-0)\hat{i}+(y-0)\hat{j}[/tex]
Magnitude is given as:
[tex]|\overrightarrow{OA}|=\sqrt{x^{2}+y^{2}}[/tex]
Direction of the vector is given as:
[tex]\theta=tan^{-1}\frac{y}{x}[/tex]
Therefore, displacement vector is:
[tex]\overrightarrow{OA}=(12-0)\hat{i}+(7-0)\hat{j}\\ \overrightarrow{OA}=12\hat{i}+7\hat{j}[/tex]
Magnitude of displacement is given as:
[tex]|\overrightarrow{OA}|=\sqrt{x^{2}+y^{2}}\\ |\overrightarrow{OA}|=\sqrt{12^{2}+7^{2}}\\ |\overrightarrow{OA}|=\sqrt{144+49}\\\\ |\overrightarrow{OA}|=13.89[/tex]
Angle of displacement is:
[tex]tan\theta=\frac{y}{x} =\frac{7}{12}\\\theta=tan^{-1}(\frac{7}{12})[/tex]
[tex]\theta=30.26[/tex]°
