`||bbv|| = 1, theta = 45^@` Find the component form of `bbv` given its magnitude and the angle it makes with the positive x-axis.

The magnitude of a vector `u = a*i + b*j` , such that:

`|u| = sqrt(a^2+b^2)`

Since the problem provides the magnitude `|v| = 1` , yields:

`1 = sqrt(a^2+b^2)`

The direction angle of the vector can be found using the formula, such that:

`tan theta = b/a`

Since the problem provides the information that the direction angle of the vector v is `theta = 45^o` , yields:

`tan 45^o= b/a => 1 = b/a => a = b`

Replacing  a for b in equation `1 = sqrt(a^2+b^2)` yields:

`1 = sqrt(a^2+a^2)=> 1 = +-a*sqrt 2 => a = +-(sqrt2)/2`

`b = +-(sqrt2)/2`

Hence, the component form of the vector v can be` <(sqrt2)/2,(sqrt2)/2> ` or `<-(sqrt2)/2,-(sqrt2)/2>.`