Check whether the three vectors $2\hat i + 2 \hat j + 3 \hat k, -3 \hat i + 3 \hat j + 2\hat k , 3\hat i + 4\hat k$ form a triangle or not.
Attempt:
$\vec{AB} = – 5\hat i + \hat j – \hat k$
And $\vec{AC} = \hat i + \hat k -2\hat j$
Therfore they form a triangle as AB and AC are not co-linear.
But textbook says,
For a triangle $\vec a + \vec b + \vec c = 0$
But for the given three vectors the sum is not zero so they do not
form a triangle.
I don't understand the error in my attempt and the way the textbook finds the right answer. Please explain the concepts involved.
Why is $\vec a + \vec b + \vec c = 0?$
Best Answer
There is a confusion between a triangle based on points and a triangle given by side vectors.
Your interpretation of the given data is that those are three points $A, B,C$.
The solution seems to indicate that the given data represents three vectors. You’re asked if those three vectors can be the sides of a triangle.