Find a vector v whose magnitude is 4 and whose component in the i direction is twice the component in the j direction.

the answer is (8√5 i + 4√5j)/5.

could someone give me a detailed explanation on how to do the problem?

A vector is an quantity which have both magnitude and direction.

Vector v is,    

Since, in the given vector v , component in the i direction is twice the component in the j direction.

Let us consider, component in j direction is x then component in i direction will be 2x.

So,  vector    

Magnitude of above vector,  <v> =

Substituting value of x in above vector equation.

We get,    

Learn more:

link

Start with

as a template for the vector . Its magnitude is 4, so

Its component in the direction is twice the component in the direction, which means

So we have

and

Lastly, rationalize the denominator:

So we end up with two possible answers,

7

step-by-step explanation: