Question

Hey, i need help with this questions. Thanks!

Answer 1

1. Approximately 5.83 units

2. Approximately 59.04°

Explanation:

Given two vectors
`\vec{u}=(5,2)` and
`\vec{v}=(2,-3).`

To find the difference
`\vec{u}-\vec{v}` just subtract coordinates of vector v from coordinates of vector u:

`\vec{u}-\vec{v}=(5-2,2-(-3))=(3,5)`

1. The magnitude of the vector
`\vec{u}-\vec{v}` is

`|\vec{u}-\vec{v}|=√(3^2+5^2)=√(9+25)=√(34)\approx 5.83\ units`

2. Find tangent of angle which vector
`\vec{u}-\vec{v}=(3,5)` forms with x-axis:

`\tan \alpha=(5)/(3)\\ \\\alpha \approx 59.04^(\circ)`