How do you find the component form of v given its magnitude 5/2 and the angle it makes with the positive x-axis is $theta=45^circ$ ?

Question

4456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-20T21:11:00

$color(blue)((5sqrt(2))/4hati+(5sqrt(2))/4hatj)$

If vector $v$ forms an angle of $45^o$ with the $x$ axis, then:

$tan(45^o)=1$

This means that a component form vector will be of the form:

$ahati +bhat(j)$ where $a=b$

We now need to find a unit vector in the direction of $v$ .

This is:

$v_2= v_1/(||v_1||)$

We will use $hati+hatj$ for $v_1$

$:.$

$v_2=(1+1)/(||1+1||)$

$||1+1||)=sqrt(2)$

So unit vector in direction of $v$ is:

$1/sqrt(2)*(hati+hatj)$

For the given magnitude of we multiply the vector by $5/2$ :

$5/2 * 1/sqrt(2) * (hati+hatj) = 5/(2sqrt(2)) * (hati+hatj)=color(blue)((5sqrt(2))/4hati+(5sqrt(2))/4hatj)$

How do you find the component form of v given its magnitude 5/2 and the angle it makes with the positive x-axis is theta=45^circtheta=45^circ?