Question

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

Answer 1

Given:

`veca` ⊥ `vecb` ⇒ `veca.vecb` = 0

|`veca` + `vecb`| = 13

`|veca|` = 5

Assuming `|vecd|` = 5 is a typo for `|veca|` = 5

Using the property `|veca + vecb|^2 = |veca|^2 + |vecb|^2`

⇒ `(13)^2 = (5)^2 + |vecb|^2`

⇒ 169 = 25 + `|vecb|^2`     ...[Simplify the squares]

⇒ `|vecb|^2 = 169 − 25`

⇒ `|vecb|^2 = 144`

⇒ `|vecb| = sqrt144`

⇒ `|vecb|` = 12