If `vec(a)` and `vec(b)` are perpendicular vectors such that `|vec(a)+vec(b)|=13 and |vec(a)|=5`, find the value of `|vec(b)|`.

Answer

`|vec(b)|=12`

Explanation

Since `vec(a) and vec(b)` are perpendicular vectors, we have `vec(a).vec(b)=0`.
Now, `|vec(a)+vec(b)|^(2)=169rArr(vec(a)+vec(b)).(vec(a)+vec(b))=169`
`rArr vec(a).vec(a)+2vec(a).vec(b)+vec(b).vec(b)=169`
`rArr |vec(a)|^(2)+|vec(b)|^(2)=169 [:. vec(a).vec(b)=0]`
`rArr 25 + |vec(b)|^(2)=169 rArr |vec(b)|^(2)=144rArr|vec(b)|=12`.