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Genrish500 [490]
3 years ago
5

Choose all statements that accurately describe properties of parallel and perpendicular lines.

Mathematics
1 answer:
KatRina [158]3 years ago
5 0

Incomplete question. I inferred you want to know the properties of parallel and perpendicular lines. Which I provided below.

<u>Explanation:</u>

In geometry, <em>parallel lines </em>are two lines that are <em>always </em><em>drawn at </em>the same distance apart and never touch each other. Parallel lines are usually denoted by the symbol ∥.

Here are some of their properties;

When a transversal intersects two parallel lines:

  • usually, the corresponding angles of the lines are equal.
  • vertically opposite angles are equal.
  • the alternate exterior angles are equal.

<em>Perpendicular lines</em><em> are two lines that </em><em>meet at a right angle (90 degrees) to each other.</em>

<em>Properties: </em>two lines that meet, implies all four angles are right angles.

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QUESTION 1
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It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is

<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)

The cosine of the angle between the vectors can be obtained from the dot product identity,

<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)   ==>   cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)

so that

<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)

For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is

<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   <em>W</em> ≈ 5.12 J

(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).

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