Question

a vector has an x-component of 19.5m and a y-component of 28.4m. Find the magnitude and direction of the vector

Answer 1

Answer:

magnitude=34.45 m

direction=$55.52\°$

Explanation:

Assuming the initial point P1 of this vector is at the origin:

P1=(X1,Y1)=(0,0)

And knowing the other point is P2=(X2,Y2)=(19.5,28.4)

We can find the magnitude and direction of this vector, taking into account a vector has a initial and a final point, with an x-component and a y-component.

For the magnitude we will use the formula to calculate the distance $d$ between two points:

$d=\sqrt{{(Y2-Y1)}^{2} +{(X2-X1)}^{2}}$ (1)

$d=\sqrt{{(28.4 m - 0 m)}^{2} +{(19.5 m - 0m)}^{2}}$ (2)

$d=\sqrt{1186.81 m^{2}}$ (3)

$d=34.45 m$ (4) This is the magnitude of the vector

For the direction, which is the measure of the angle the vector makes with a horizontal line, we will use the following formula:

$tan \theta=\frac{Y2-Y1}{X2-X1}$  (5)

$tan \theta=\frac{24.8 m - 0m}{19.5 m - 0m}$  (6)

$tan \theta=\frac{24.8}{19.5}$  (7)

Finding $\theta$:

$\theta= tan^{-1}(\frac{24.8}{19.5})$  (8)

$\theta= 55.52\°$  (9) This is the direction of the vector