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:
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Answer:
They are similar by the definition of similarity in terms of a dilation.
Step-by-step explanation:
Given:
The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0).
To choose: the correct option
Solution:
According to distance formula distance between points is given by
For ΔMNO,
For ΔPQR,
So,
Therefore, They are similar by the definition of similarity in terms of a dilation.
Two triangles are said to be similar if their sides are proportional.