Q.Check whether the vectors $2\hat i+2\hat j+3\hat k$, $-3\hat i+3\hat j+2\hat k$ and $3\hat i+4\hat k$ form a triangle or not.

Let $\bar p=2\hat i+2\hat j+3\hat k,\ \bar q=-3\hat i+3\hat j+2\hat k,\ \bar r=3\hat i+4\hat k$. If these three

vectors, taken in order, are to represent the sides of a triangle (tip-to-tail, returning to the start), their

sum must be the zero vector, since going around a closed triangle by the triangle/polygon law always returns

to the starting point.

Adding component-wise:

$\bar p+\bar q+\bar r=(2-3+3)\hat i+(2+3+0)\hat j+(3+2+4)\hat k=2\hat i+5\hat j+9\hat k.$ …

Recall that vectors representing the sides of a triangle (traversed consistently) must sum to zero; add the g …

Checking only that the magnitudes could plausibly form a triangle (triangle inequality on lengths) instead of the correct …