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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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Solve the absolute value equation or indicate that the equation has no solution. |x-5|=4
Lelu [443]

Step-by-step explanation:

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3 0
1 year ago
The YMCA lap pool is a right rectangular prism 36.8\, \text{m}36.8m36, point, 8, start text, m, end text long by 20 \,\text{m}20
PilotLPTM [1.2K]

Volume is a three-dimensional scalar quantity. The depth of the YMCA lap pool is 2 meters.

<h3>What is volume?</h3>

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given that the following details about the YMCA lap pool:

  • The volume of the pool = 1472m³
  • The length of the pool = 36.8m
  • The width of the pool = 20 m

Since the pool is in the space of a right rectangular prism, therefore, the volume of the prism will be the product of length, width and depth. Therefore, the volume of the pool can be written as,

The volume of the pool = Length × width × depth

1472m³ = 36.8m × 20 m × depth of the pool

Depth of the pool = (1472m³ ) / (36.8m × 20m)

                              = 2 meter

Hence, the depth of the YMCA lap pool is 2 meters.

Learn more about Volume here:

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3 0
1 year ago
Pls give me an answer to this!!!!!!!
gayaneshka [121]

Answer:

  1. CONSTRUCT FROM A TO B AND ALSO A TO C AND B TO C
5 0
3 years ago
Determine the solution to f(x) = g(x) using the following system of equations: (5 points) f(x) = 3x − 23 g(x) = −4.5x + 7
jeka94

Answer:

(The solution is (4, -11).

Step-by-stp explanation:

Let f(x) = g(x) = y:

y = 3x − 23

y = -4.5x + 7     Subtract the second equation from the first to eliminate y:

0 = 7.5x - 30

7.5x = 30

x = 4

Plug this into the first equation:

y = 3(4) - 23

y =  -11.

5 0
3 years ago
What is the slope formula of (4,2) and (7, 6.5)
Lady_Fox [76]

Suppose the given coordinates are represented as,

\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}

Then, the formula for slope can be expressed as,

\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}

Solving it,

m=\frac{4.5}{3}=1.5

The slope is 1.5.

The formula of (10, 8) anjd (-5,8) is

m=\frac{8-8}{-5-10}

3 0
1 year ago
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