What are the coordinates of point B on AC such that the ratio of AB to AC is 5 : 6?

B

=(x

A

+

6

5

⋅(x

C

−x

A

),y

A

+

6

5

⋅(y

C

−y

A

),z

A

+

6

5

⋅(z

C

−z

A

))

Step-by-step explanation:

Let suppose that A, B, and C have the following points with respect to origin in the Euclidean space:

\vec A = (x_{A}, y_{A}, z_{A})

A

=(x

A

,y

A

,z

A

)

\vec B = (x_{B}, y_{B}, z_{B})

B

=(x

B

,y

B

,z

B

)

\vec C = (x_{C}, y_{C}, z_{C})

C

=(x

C

,y

C

,z

C

)

Besides, let consider that locations of A and B are currently known. The ratio is:

\frac{AB}{AC} = \frac{5}{6}

AC

AB

=

6

5

AB = \frac{5}{6} \cdot ACAB=

6

5

⋅AC

Vectorially speaking, expression can be rewritten in the following terms:

\overrightarrow{AB} = \frac{5}{6}\cdot \overrightarrow{AC}

AB

=

6

5

⋅

AC

(x_{B}-x_{A}, y_{B}-y_{A}, z_{B}-z_{A}) = \frac{5}{6}\cdot (x_{C}-x_{A}, y_{C}-y_{A}, z_{C}-z_{A})(x

B

−x

A

,y

B

−y

A

,z

B

−z

A

)=

6

5

⋅(x

C

−x

A

,y

C

−y

A

,z

C

−z

A

)

Now, each side of the equation is summed vectorially by \vec A

A

and coordinates of point B are finally found:

\vec B = \left(x_{A}+\frac{5}{6}\cdot (x_{C}-x_{A}), y_{A}+\frac{5}{6}\cdot (y_{C}-y_{A}), z_{A}+\frac{5}{6}\cdot (z_{C}-z_{A})\right)

B

=(x

A

+

6

5

⋅(x

C

−x

A

),y

A

+

6

5

⋅(y

C

−y

A

),z

A

+

6

5

⋅(z

C

−z

A

))

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

can i have brainliest

pi x^2

step-by-step explanation:

pi times x squared