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Marina86 [1]
3 years ago
7

Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

Mathematics
1 answer:
tester [92]3 years ago
5 0

The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)

This is the vector equation; getting the parametric form is just a matter of delineating

<em>x</em>(<em>t</em>) = 1 + <em>t</em>

<em>y</em>(<em>t</em>) = 3<em>t</em>

<em>z</em>(<em>t</em>) = 6 + <em>t</em>

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bogdanovich [222]

Answer:

AE=22.4

Step-by-step explanation:

BE is 1/2 of BC

BC is 20 cm                 All sides of a square are equal

BE = 1/2 BC                  Property of a midpoint.

BE = 10

Now just use Pythagorus

AB^2 + BE^2 = AE^2

AE^2 = 20^2 + 10^2   Perform the sqrs

AE^2 = 400 + 100      Add the terms

AE^2 = 500                Take the square root of both sides

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6 0
3 years ago
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kiruha [24]
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The probability will always be 50%
3 0
3 years ago
Find a and b to make the following matrices equal.
podryga [215]
We need the following to be true
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Let's look at the first equation.
a + 2b = -a
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Substitute b= -a into the second equation
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Just take the negative of that and you get the value of b.
b = -1

Your solution is a=1 and b = -1.

Have an awesome day! :)
4 0
3 years ago
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Korvikt [17]
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A = 84
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3 years ago
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