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harina [27]
3 years ago
10

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.

Mathematics
1 answer:
alex41 [277]3 years ago
8 0

Answer:

The answers are given in the attachment

Step-by-step explanation:

The detailed step by step calculations are shown in the attachment.

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