Determine the area of the triangle that is made up by the

Question

Position Vector Characteristics Three position vectors r₁ = OA, r₂ = DB, and r₃ = EB are illustrated in Figure 1.31.

(a) Determine the length of OA, DB, and EB.

(b) Determine the directional cosines of OA, DB, EB, and AO, BD, and BE.

(c) Determine the angle between OA and DB.

(d) Determine a vector to be perpendicular to both OA and DB.

(e) Determine the surface area of the box by using the vectors OA, DB, and EB.

(f) Determine the volume of the box by using the vectors OA, DB, and EB.

(g) Determine the equation of the perpendicular plane to OA, DB, and EB.

(h) Determine the area of the triangle that is made up by the intersection of the planes in (g) if the plane of OA includes point O, the plane of DB includes point D, and the plane of EB includes point E.