Answer
$98i + 269.5j – 199.5k$
Work Step by Step
Given that,
Magnitude of $F = 350 lb$
To express the Force as a cartesian vector, we first find the direction vector of $\overrightarrow{AB}$
Position vector of $A = 0i + 0j + 35k$
Position vector of $B = 50sin(20°)i + 50cos(20°)j = 17.10i + 46.98j$
Direction vector of $\overrightarrow{AB} = B – A = [ 17.10i + 46.98j ] – [35k] = 17.10i + 46.98j -35k$
Now, we find a unit vector in the direction of AB
Magnitude of $\overrightarrow{AB} = \sqrt (17.10^2 + 46.98^2 + 35^2) = 61.03$
$∴$ Unit vector in direction of $\overrightarrow{AB} = \frac{1}{61.03}(17.10i + 46.98j – 35k) = 0.28i + 0.77j – 0.57k$
Thus, force $F$ can be expressed in Cartesian coordinates as
$(350)(0.28i + 0.77j – 0.57k) = 98i + 269.5j – 199.5k$
