8. Let α, β, γ be the angles made by a vector u ∈ R 3 with positive x, y, z−axis respectively. Then, the numbers l = cos α, m =
cos β, n = cos γ are called the direction cosines of u.
(a) Find the formulas for the direction cosines: l, m, n of the vector u = hu1, u2, u3i.
(b) Prove that l 2 + m2 + n 2 = 1.
(c) Find the direction cosines l, m, n of the vector u = h1, −1, 1i.
(a) Find the formulas for the direction cosines: l, m, n of the vector u = hu1, u2, u3i.
(b) Prove that l 2 + m2 + n 2 = 1.
(c) Find the direction cosines l, m, n of the vector u = h1, −1, 1i.
1 answer:
You might be interested in
Answer:
Ben = $ 41
Kaden = $ 31
Step-by-step explanation:
Let initially Ben has $ p and then Kaden has $ (p - 10).
After that
Ben has= $ (p + 4)
Kaden has = $ (p- 10 + 4) = $ ( p - 6)
According to the question,
Initially Ben has $ 41 and Kaden has $ 31.