Question

20 point question

Suppose u and v are orthogonal vectors with ||u|| =5. ||u||= 1/2 ||v||, find ||u+v||.​

Answer 1

Explanation:

`|| \overrightarrow {u}||=5\\\\|| \overrightarrow {u}||=\frac{|| \overrightarrow {v}||}{2} \Longrightarrow\ || \overrightarrow {v}||=2*|| \overrightarrow {v}|=10\\\\|| \overrightarrow {u}+\overrightarrow {v}||^2=|| \overrightarrow {u}||^2+|| \overrightarrow {v}||^2+0\ (since\ u\ and\ v\ are\ orthogonal\ vectors \ )\\\\=5^2+10^2=125\\\\|| \overrightarrow {u}+\overrightarrow {v}||=5*√(5) \\`

Answer 2

`5√(5)`

Explanation:

See attached image.

The vectors u and v are orthogonal, so the angle between them measures
`90^\circ`.
`||u||=5` and
`||u||=(1)/(2)||v|| \Rightarrow ||v||=10`

The vector sum is the diagonal shown in the image and its length/magnitude/norm can be found by using the Pythagorean Theorem.

`||u+v||=√(5^2+10^2)=√(125)=5√(5)`