VECTORS-Which is the largest internal angle of the triangle?

Consider the triangle ABC with vertices A(-6, -4, -2), B(-5, -5, -7), and C(-1, 4, -4). Which is the largest internal angle of the triangle?





ABC, BCA, or CAB?





WHAT is the size of this angle...?





HELP!

VECTORS-Which is the largest internal angle of the triangle?
So, there are a few ways to do this problem.





The easiest is to decide which side of the triangle is the longest. Then of course the opposite angle to that side is the largest angle.





To finish the problem you have to actually calculate the angle. This is done using the dot product. You should know that for two vectors a and b





a.b = |a|*|b|*cos(p)





where p is the angle between a and b. Here I'm using . for the dot product and | | for the length of a vector. Thus in order to find p you can use the formula





acos(a.b/(|a|*|b|)) = p
Reply:no worries. i got the answer :D haha Report It

Reply:I’d better do like this:


Vector AB = (-5+6, -5+4, -7+2) = (1, -1, -5), |AB|^2 = 27;


Vector AC = (-1+6, 4+4, -4+2) = (5, 8, -2), |AC|^2= 25+64+4 = 93


Vector BC = (-1+5, 4+5, -4+7) = (4, 9, 3), |BC|^2 = 16+81+9 = 106


The longest side is opposite of biggest angle; thus angle A is the biggest!





Added:


(AB*AC) = 1*5 – 1*8 + 5*2 = 7 = |AB|*|AC|*cos(A) = 50.11*cos(A), hence cos(A)=0.14 %26gt;0 thus A=82°