Question

Find the direction cosines of the sides of the triangle whose vertices are (3, 5, - 4), (- 1, 1, 2) and (- 5, - 5, - 2).

Answer 1

Answer:

Step-by-step explanation:

Let A(3,5,-4)B(-1,1,2)C(-5,-5,2)

Direction ratio of AB=((3--1)(5-1)(-4-2))

=(4,4,-6)

So direction cosine=({4/√(4^2 +4^2 +(-6)^2)} , {4/√(4^2 +4^2 +(-6)^2)} ,

{-6/√(4^2 +4^2 +(-6)^2)})

=( 4/√68 , 4/√68 , -6/√68)

Similarily

DR of BC=((-1-5)(1--5)(2-2))=(-6,6,0)

Direction cosine of BC=(-1/√2,1/√2,0)

&

DR of CA=((-5-3)(-5-5)(2--4))=(-8,-10,6)

Direction cosine of CA=(-8/√200 , -10/√200 ,6/√200)

Hope this helps