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worty [1.4K]
3 years ago
8

Three vectors A, B, C in three-dimensional space satisfy the following properties

Mathematics
1 answer:
wlad13 [49]3 years ago
3 0

Answer:

\frac{7}{8}\pi

Step-by-step explanation:

observe

||a–b+c|| = ||a+b+c||

(a-b+c)² = (a+b+c)²

(a+b+c)² – (a-b+c)² = 0

((a+b+c)+(a-b+c))((a+b+c)–(a-b+c)) = 0

(2a+2c)(2b) = 0

(a+c)b = 0

a•b + c•b = 0

||a||×||b||×cos(π/8) + ||c||×||b||×cos(θ) = 0

\cos(\theta)=-\frac{||a||\times ||b|| \times \cos(\frac{\pi}{8})}{||c||\times ||b||}=-\cos(\frac{\pi}{8})\\ \theta=\frac{7}{8}\pi

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Answers: Angle A is 36 degrees, angle C is 54 degrees

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Work Shown:

The angles A and C are complementary, meaning they add to 90 degrees.

(Angle A) + (Angle C) = 90

(2x-4) + (2x+14) = 90

(2x+2x)+(-4+14) = 90

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4x+10-10 = 90-10 .... subtract 10 from both sides

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If x = 20, then,

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3 years ago
The value of x for which 3 (x-2) = 2 (x+1)​
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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
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Step-by-step explanation:

<u>Step 1: Define equation</u>

3(x - 2) = 2(x + 1)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                     3x - 6 = 2x + 2
  2. Subtract 2x on both sides:          x - 6 = 2
  3. Add 6 to both sides:                    x = 8

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    3(8 - 2) = 2(8 + 1)
  2. Subtract/Add:                      3(6) = 2(9)
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Here we see that 18 does indeed equal 18.

∴ x = 8 is a solution to the equation.

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