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Kobotan [32]
3 years ago
13

Helllohello help please if you want -

Mathematics
1 answer:
uranmaximum [27]3 years ago
6 0

3(7d + 4e) = 3 • 7d + 3 • 4e = <u>21d</u><u> </u><u>+</u><u> </u><u>12e</u>

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Answer choice A is correct
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Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
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Answer:

\frac{7}{\sqrt{3}}

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |                   --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |

d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |

d = |\frac{(-7)}{\sqrt{3}} |

d = \frac{7}{\sqrt{3}}

Therefore, the shortest distance from the point to the plane is  d = \frac{7}{\sqrt{3}}

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