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

magnitude=34.45 m

direction=
`55.52\°`

Step-by-step 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=(Y2-Y1)/(X2-X1)` (5)

`tan \theta=(24.8 m - 0m)/(19.5 m - 0m)` (6)

`tan \theta=(24.8)/(19.5)` (7)

Finding
`\theta`:

`\theta= tan^(-1)((24.8)/(19.5))` (8)

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