Knowing the tension in cable AD is $280$ lb $.$ and the distance a is $3\mathrm{.}5$ ft $,$ determine the projection on AB of the force exerted by cable AC at point $\backslash ($ A $\backslash )$ by both methods below.

a$)$ Using angle BAD

Projection of tension in cable AD onto rod $\backslash (\backslash$mathrm$\{$AB$\}=\backslash )$

lb$.$ directed from A towards B

b$)$ Using dot $($scalar$)$ product

Unit vector from point $\backslash ($ A $\backslash )$ to point $\backslash ($ D$=\backslash )$

Force vector of cable $\backslash ($ A D $\backslash )$ acting on point $\backslash ($ A$=\backslash )$

Unit vector from point $\backslash ($ A $\backslash )$ to point $\backslash ($ B$=\backslash )$

$\backslash (1+\backslash )$

lk

$\backslash (\backslash$mathrm$\{$lbj$\}-\backslash )$

lbk

Scalar $($dot$)$ product of the force and appropriate unit vector:

lb$.$ directed from A towards B