Question

Let the vector \mathbf{v}v have an initial point at (1, -2)(1,−2) and a terminal point at (0, 0)(0,0). Plot the vector \mathbf{v}v and afterwards follow the guided steps to analyze the vector.

Answer 1

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, $\vec{v}$, has been shown in the figure.

The magnitude of the vector:

$|\vec{v}|=\sqrt{(1-0)^2+(-2-0)^2}=\sqrt{1+4}=\sqrt{5}$

The direction of a vector is the angle made by a vector with the positive direction of the x-axis.

From the figure, $\theta = 180 \degree\tan ^{-1} \left|\frac {0-(-2)}{0-1}\right|$

$\theta = 180 ^{\circ} - \tan^{-1}(2) = 180 ^{\circ} - 63.43^{\circ}$

$\theta =116.57 ^{\circ}$

Hence, the required vector having a magnitude $\sqrt {5}$ and direction $116.57 ^{\circ}$ has been shown in the figure.