How do you ind the vector? (Precalculus)?

Question

For example, magnitude [[v]]=7, and the direction of u=3i+4j. This is given, and the question asks for the vector v, that is in the same direction as u, using the given magnitude.

How do you solve this?

Answer 1

The magnitude of u is:

║u║ = √(3² + 4²) = √(9 + 16) = √25 = 5

So to find a unit vector in the same direction of u, divide u by its own magnitude:

u/║u║ = 1/5(3 i + 4 j) = 3/5 i + 4/5 j

And then to find a vector with the same direction and magnitude 7, just mulitply the unit vector by 7:

7u/║u║ = 21/5 i + 28/5 j = 4.2 i + 5.6 j

Answer 2

|| u || = ||3i + 4j|| = || (3,4) ||
= sqrt(3^2 + 4^2) = sqrt(25) = 5