Question

Find the component form of v given its magnitude and the angle it makes with the positive x-axis, and sketch v. ||v||=3, v in the direction 3i+4j

Answer 1

All we have to do is find the magnitude of 3i + 4j
that is, of course √3² + 4²) = √(9+16) =√25 = 5

then normalize it.

That gives us a vector of magnitude 1 and that vector is

3........4
--- i + -----j
5........5

now, all we have to do is multiply the coefficients by 3 in order to triple the magnitude of the unit
vector to 3, that gives us

v is equal to

9.......12
--- i + -----j
5........5

Answer 2

v=(9i+12j)/5