Let a = (1, 0, 3) and b = (−3, 2, 1).

(a) (3 points) normalize −−→ab.
(b) (3 points) find the midpoint m of the segment ab.
(c) (4 points) find equation of the plane passing through m and perpendicular to ab

a)

b)

c)

Step-by-step explanation:

a)

AB, OB, OA are vectors.

Normalizing AB:

b)

OM, OA, OB are vectors.

So,

c)

Hence,

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

66.666666667%

step-by-step explanation:

divide 150 by 100

divide 100 by 1.5

there you go!

decreased by 33.333333334%