Question

If i have A(-2,4,1), B(3,5,8), and C(-4,7,3) how do i find the angle ABC?

Answer 1

is their a formula?

Answer 2

Simply write the equation of lines AB and BC.Then find angle between them

Answer 3

how would i calculate the equations?

Answer 4

we find the vectors by subtracting the corresponding co-ordinates
\[
\vec{AB}=[3-(-2)]\hat{i}+(5-4)\hat{j}+(8-1)\hat{k}\\
\vec{AB}=5\hat{i}+1\hat{j}+7\hat{k}
\]similarly, we find \(\vec{BC}\)

Answer 5

^^

Answer 6

and then i would just find the angle between them?

Answer 7

yep

Answer 8

and how would i do that?

Answer 9

first, show me your vcetor BC

Answer 10

-7i + 2j - 5k

Answer 11

remember the DOT PRODUCT of vectors?
using that:
\[
\vec{AB}\cdot\vec{BC}=|\vec{AB}||\vec{BC}|\cos\theta\\
\cos\theta=\frac{\vec{AB}\cdot\vec{BC}}{|\vec{AB}||\vec{BC}|}
\]

Answer 12

good. then you'd need to find their magnitudes

Answer 13

okay! i see! i get it know! thank you so much!

Answer 14

you are welcome