Draw the resultant vector for the pair of vectors with angle α between them using the given information.

|a| = 7, |b| = 15, α = 54°

Two Siberian Huskies are pulling a sled on a snowy terrain. The forces exerted by these dogs on the sled are 16 lb, and 5 lb, and the angle between these forces is 18.3°. Determine the magnitude of the equilibrant and the angle it makes with the 16 lb force.

A motorboat departs 10.4 miles out of port with a bearing of 313°. After a few hours, the motor makes a turn and starts moving to the west for 6.9 mi. Find the bearing of the ship and its distance from the port.

A vector $a$ starts at $P_1$ and ends at $P_2$. Express the vector $a$ in terms of $i$ and $j$.

$P_1=(-31,44)$, $P_2=(35,-28)$

For the given vector, calculate its magnitude and direction angle. Express your answer to the nearest tenth, if required.

$〈28\sqrt3,-28\sqrt3〉$

Given the following vector, $\mathbf{v}$, obtain the unit vector that aligns with the direction of $\mathbf{v}$.

$\mathbf{v}=-\mathbf{i}-\sqrt3\mathbf{j}$

Are the vectors a and b orthogonal?

a = 18i, b = -7i

Assess whether a and b are parallel, orthogonal, or do not possess either property. 

a = 17i -24j, b = 85i -120j

Determine the projection of vector a onto vector b. Next, express vector a as vectors, a₁ and a₂, where a₁ is parallel to vector b and a₂ is perpendicular to vector b. 

a = 12i +5j, b = 2i +6j