Given that the initial point of the vector is (1,-2) and the termination point of the vector is (0,0).
So, the tail of the vector is at point (1,-2) and the head of the vector is at (0,0). The vector, [tex]\vec{v}[/tex], has been shown in the figure.
The magnitude of the vector:
[tex]|\vec{v}|=\sqrt{(1-0)^2+(-2-0)^2}=\sqrt{1+4}=\sqrt{5}[/tex]
The direction of a vector is the angle made by a vector with the positive direction of the x-axis.
From the figure, [tex]\theta = 180 \degree\tan ^{-1} \left|\frac {0-(-2)}{0-1}\right|[/tex]
[tex]\theta = 180 ^{\circ} - \tan^{-1}(2) = 180 ^{\circ} - 63.43^{\circ}[/tex]
[tex]\theta =116.57 ^{\circ}[/tex]
Hence, the required vector having a magnitude [tex]\sqrt {5}[/tex] and direction [tex]116.57 ^{\circ}[/tex] has been shown in the figure.
