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Ulleksa [173]
3 years ago
10

Find an equation of the plane orthogonal to the line

Mathematics
1 answer:
jolli1 [7]3 years ago
4 0

The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.

The tangent vector for the line is

d/d<em>t</em> (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩<em>t </em>) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has equation

⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it standard form gives

⟨<em>x</em> - 9, <em>y</em> - 6, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

7 (<em>x</em> - 9) - 7 (<em>y</em> - 6) - 6<em>z</em> = 0

7<em>x</em> - 63 - 7<em>y</em> + 42 - 6<em>z</em> = 0

7<em>x</em> - 7<em>y</em> - 6<em>z</em> = 21

so that

<em>a</em> = 7, <em>b</em> = -7, <em>c</em> = -6, and <em>d</em> = 21

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Grace earns $7 for each car she washes. She always saves $25 of her weekly earnings.This week,she wants to have at least $65 in
Irina-Kira [14]

Answer:

she must wash 8 cars because 7 x 8 = 56 so yeah bye

Step-by-step explanation:


7 0
3 years ago
Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).
vivado [14]

The equation of the line is y=\frac{1}{4}x-\frac{29}{7}

Explanation:

The equation of the line is perpendicular to y=-14 x-8

The equation is of the form y=mx+b where m=-14

<u>Slope:</u>

The slope of the perpendicular line can be determined using the formula,

m_1 \cdot m_2=-1

-14 \cdot m_2=-1

       m_2=\frac{1}{14}

Thus, the slope of the line is m=\frac{1}{14}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the slope m=\frac{1}{14} and the point (2,-4), we get,

y+4=\frac{1}{14}(x-2)

Simplifying, we get,

y+4=\frac{1}{14}x-\frac{1}{7}

     y=\frac{1}{14}x-\frac{1}{7}-4

     y=\frac{1}{4}x-\frac{29}{7}

Thus, the equation of the line is y=\frac{1}{4}x-\frac{29}{7}

3 0
3 years ago
What are opposites?
Scrat [10]

Answer:

Opposites are basically the negative and positive of a number.  I cannot think of something for a real world situation though.

Step-by-step explanation:

3 0
3 years ago
A 4-lb. force acting in the direction of (vector) 4,-2 moves an object just over 7ft from point (0,4) to (5,-1). Find the work d
Tcecarenko [31]

To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.

The work done on moving the object is 27ft*lbs

<h3>Work done in moving the object from point A to point B</h3>

To find the work done on this object, let's find the net force on the object.

Data;

  • force = 4lb
  • direction = 4, -2
  • displacement = 7ft
  • direction = (0, 4) to (5,1)

The unit vector of the force is

\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}

\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }

The net force acting on the object is

F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )

The displacement on the object is 7ft through (0,4) to (5, -1)

The unit vector on displacement is

\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}

\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }

The net displacement will be

7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}

The work done will be F.d

w = f. d \\

w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs

The work done on moving the object is 27ft*lbs

Learn more on work done on an object here;

brainly.com/question/26152883

#SPJ1

6 0
2 years ago
What is the solution of this question.<br> 9988 ÷ 23 =
gizmo_the_mogwai [7]

Answer:

434\frac{6}{23}  

I hope this helps!

4 0
3 years ago
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