Question

If `veca and vecb` are perpendicular vectors, `|veca+vecb| = 13 and |veca| = 5` ,find the value of `|vecb|.`

Answer 1

Given that `veca and vecb` are two perpendicular vectors.

Thus, ` veca .vecb= 0 `
Also given that, ` |veca +vecb| 13 and |veca|=5.`

We need to find the value of vecb.

Consider `|veca + vecb|^2 :`

`|veca +vecb|^2 = |veca|^2 |veca.vecb|+|vecb|^2`

`13^2=5^2+2xx0+|vecb|^2`

`169=25+|vecb|^2`

`|vecb|^2=169-25`

`|vecb|^2=144`

`vecb=12`