Consider the vector 𝐴⃑ in the first quadrant, with magnitude

Question

given by 𝐴 = 10, that makes an angle of 𝜃 = 25° with the 𝑥-
axis.

(a) Find a vector, 𝐵⃑⃑, such that 𝐴⃑ + 𝐵⃑⃑ = 0. What is the
magnitude of 𝐵⃑⃑? Carefully sketch both 𝐴⃑ and 𝐵⃑⃑, making
sure they are proportional.
(b) Find a unit vector, 𝑢̂, such that 𝐴⃑ ⋅ 𝑢̂ = 0.
(c) Let 𝑉⃑⃑ = 5 x̂ − 7 ŷ. Compute 𝐴⃑ × 𝑉⃑⃑ and 𝑉⃑⃑ × 𝐴⃑. Compare your answers; does this make sense?

Answer 1

(a) clearly, B = -A
(b) u must point in a direction 25±90°, right?
so figure the x and y components
(c) I assume you can figure the cross product. Your calculations should verify that AxV = -(VxA)
(you know that switching rows in a determinant changes its sign, right?)