Is Triangle ABC a Right Triangle?

[spoc21]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as I'm not sure if this is the correct approach..
any help is much appreciated

thanks..

 

[justsof]

I think it is the right approach, but ask yourself; why are you using the dot product? Is there a property of the dot product that you can use? And what does it mean if this product is zero?

 

[spoc21]

I think it is the right approach, but ask yourself; why are you using the dot product? Is there a property of the dot product that you can use? And what does it mean if this product is zero?

yep..If the dot product is 0, it means that there is a right angle present between A, and B, since cos(inverse) 0 = 90...I was just confused about my method, is this correct, or should I be using vectors AB, BC, and AC...

 

[Mark44]

You should be using the vectors that represent the sides of the triangle. What you have found is that the vectors to vertices A and B happen to be perpendicular, but that doesn't say anything about the sides of this triangle.

 

[spoc21]

You should be using the vectors that represent the sides of the triangle. What you have found is that the vectors to vertices A and B happen to be perpendicular, but that doesn't say anything about the sides of this triangle.

ok so we find values of sides AB, BC, and AC right?...Ive gotten that AB = [-6,0,-6]..BC =[-1,4,7]..and AC = [-7,4,-13]...but now none of the dot products are equal to 0...so its getting more confusing..but is this correct?

thanks,

 

[Mark44]

Your work and mine agree. Are you sure you copied the problem correctly?

 

[spoc21]

yep, the question again is: Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a right triangle, explain using the vector mehtod..

so basically we can conclude ABC is not a right triangle?, since the dot product is not 0, illustrating that there is no right angle..

 

[Mark44]

Pretty much. ABC is not a right triangle because no two sides are perpendicular. You don't want to say "since the dot product is not 0" because you calculated three dot products to reach this conclusion.

 

[spoc21]

Also, I calculated the values of sides AB, etc. using the formula [(b1-a1), (b2-a2), (b3-a3)] so [(-2-4), (1-1), and (1-7)]

[-6,0,-6]

 

[Mark44]

Of course. That's how you get the vectors to dot with each other.

using the formula [(b1-a1), (b2-a2), (b3-a3)] so [(-2-4), (1-1), and (1-7)]

[-6,0,-6]

Don't put anything like the above in your work that you hand in, since it's gobbledy-gook. I believe you know what you're doing in this problem, and I understant what you mean, but you're not writing what you mean. You don't have to say "using the formula ..." Your instructor understands how to get the vector that joins two points.

"so [(-2-4), (1-1), and (1-7)]" does what? is what? What's the rest of this thought?

"[-6,0,-6]" This vector equals the one in the previous line, so connect the two with =.

 

[spoc21]

this is just rough work, I have completed the question neatly, using proper notation..
but its correct that AB = [-6,0,-6] right?

Thanks,

 

[Mark44]

right

 

[spoc21]

ok thanks, your help is much appreciated..