Question

Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6),

a. Determine the perimeter of ΔABC, correct to one decimal place;

b. Is triangle ABC a right triangle? Explain using the vector method.

Answer 1

i dont spose you know what a dot product of vector is?

Answer 2

to some extent.

Answer 3

ah, it even says using vectors ...

create 3 vectors:

A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)
-4-1-7 -4-1-7 -4 -1 -7
-----------------------------------
0 0 0 -6 0 -6 -7 4 -13

and we need one more between B and C

B(-2, 1, 1) and C(-3, 5, -6)
2 -1 -1 2 -1 -1
-----------------------
0 0 0 -1 4 -7

Answer 4

we need to test 3 possibilities

a.b
a.c
b.c

Answer 5

a.b a.c b.c
-1 4 -7 -1 4 -7 -6 0 -6
-6 0 -6 -7 4 -13 -7 4 -13
---------------------------------
6+0+42 7+16+.... 42+0+.... none of these zero out do they

Answer 6

dot each vector to itslef and sqrt it to determine length

Answer 7

-1 4 -7 -6 0 -6 -7 4 -13
-1 4 -7 -6 0 -6 -7 4 -13
------------------------------------
1+16+49 36+36 49+16+169 sqrt the results and add em up

Answer 8

thanks

Answer 9

yw