Question

Vectors ⃗ and ⃗ lie in the ‑plane. Vector ⃗ has a magnitude of 13.6 and is at an angle of 130.5∘ counterclockwise from the + ‑axis. Vector ⃗ has a magnitude of 24.1 and is 230.3∘ from the + ‑axis. Resolve ⃗ and ⃗ into components, and express using unit vectors, ⃗=i+ j, ⃗=k+ l where i, j, k, and l are the calculated values of the ‑, ‑, and ‑components of vectors ⃗ and ⃗, respectively.

a) i, j, k, l
b) x, y, z, w
c) a, b, c, d
d) u, v, w, x

Answer 1

Vectors ⃗ and ⃗ are resolved into components along the coordinate axes using the standard notation i, j, k, and l for x, y, z, and w, respectively. This simplifies representation and manipulation in vector analysis.

a) i, j, k, l

Step-by-step explanation:

In vector analysis, resolving vectors into components is a common technique. Vector ⃗ with a magnitude of 13.6 and an angle of 130.5° counterclockwise from the + ‑axis can be expressed as ⃗ = 13.6(cos 130.5° i + sin 130.5° j), where i and j are the unit vectors along the x and y axes, respectively.

Similarly, vector ⃗ with a magnitude of 24.1 and an angle of 230.3° from the + ‑axis can be expressed as ⃗ = 24.1(cos 230.3° i + sin 230.3° j).

In this context, the notation i, j, k, and l is commonly used to represent the components along the x, y, z, and w axes, respectively. Therefore, expressing ⃗ and ⃗ using unit vectors is denoted as ⃗ = i + j and ⃗ = k + l.