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insens350 [35]
3 years ago
14

Let A = (1, 0, 3) and B = (−3, 2, 1).

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
5 0

Answer:

a) (-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})

b) (-1,1,2)

c) -2x+y-z=1

Step-by-step explanation:

a)

AB, OB, OA are vectors.

AB = OB - OA = (-3, 2, 1) - (1, 0, 3) = (-4, 2, -2)\\||AB|| = \sqrt{(-4)^2+2^2+(-2)^2}=\sqrt{24}\\

Normalizing AB: \frac{AB}{||AB||} = (\frac{-4}{\sqrt{24}},\frac{2}{\sqrt{24}}, \frac{-2}{\sqrt{24}})=(-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})

b)

OM, OA, OB are vectors.

OM = \frac{1}{2}OA+\frac{1}{2}OB=(\frac{-3+1}{2} ,\frac{2+0}{2}, \frac{1+3}{2} )=(-1,1,2)

So, M = (-1,1,2)

c)

-4x+2y-2z=(-4)(-1)+(2)(1)+(-2)(2)=4+2-4=2

Hence,

-2x+y-z=1

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