Question

Vector u has its initial point at (17, 5) and its terminal point at (9, -12). Vector v has its initial point at (12, 4) and its terminal point at (3, -2). Find ||3u − 2v||.

Answer 1

`||3u-2v||=39.4588`

Explanation:

Vector u can also be written with initial point at the origin as:

`u=(9-17,-12-5)\\u=(-8,-17)`

and vector v in a similar way can be written as:

`v=(3-12,-2-4)\\v=(-9,-6)`

then the new vector created via the operations: 3u -2v, can be expressed as:

`3u-2v=3\,(-8,-17)-2\,(-9,-6)\\3u-2v=(-6,-39)`

Now the norm of this vector can be found using the Pythagorean identity:

`||3u-2v||=||(-6,-39||=√((-6)^2+(-39)^2) =39.4588`