`||bbv|| = 7/2, theta = 150^@` 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| = 7/2` , yields:

`7/2 = 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 direction angle` theta = 150^o` , yields:

`tan 150^o = b/a `

`tan 150^o = tan(180^o - 30^o) = (tan 180^o - tan 30^o)/(1 + tan 180^o* tan 30^o) = -tan 30^o`

`tan 150^o = -sqrt3/3 => b/a = -sqrt3/3 => b = -a*sqrt3/3`

Replacing `-a*sqrt3/3` for b in equation `7/2 = sqrt(a^2+b^2)` yields:

`7/2 = sqrt(a^2+a^2/3)=> 7/2 = +-2a/sqrt3 => 4a = +-7sqrt3 => a = +-(7sqrt3)/4`

`b = +-7/4`

Hence, the component form of the vector v can be `<(7sqrt3)/4,-7/4> ` or `<-(7sqrt3)/4,7/4>.`