20 point question

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

The vectors u and v are orthogonal, so the angle between them measures [tex]90^\circ[/tex]. [tex]||u||=5[/tex] and [tex]||u||=\frac{1}{2}||v|| \Rightarrow ||v||=10[/tex]

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

[tex]||u+v||=\sqrt{5^2+10^2}=\sqrt{125}=5\sqrt{5}[/tex]

Answer Link

caylus caylus · Answer 2 · 2021-08-21T17:16:21+02:00

Answer:

Step-by-step explanation:

[tex]|| \overrightarrow {u}||=5\\\\|| \overrightarrow {u}||=\dfrac{|| \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*\sqrt{5} \\[/tex]

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

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20 point question

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