Show that the vectors vector a = 3i - 2j + k, vector b = i - 3j + 5k, vector c = 2i + j - 4k form a right angled triangle.

Question

Show that the vectors  \(\vec a=3\hat i-2\hat j+\hat k,\)  \(\vec b=\hat i-3\hat j+5\hat k,\)  \(\vec c=2\hat i+\hat j-4\hat k\)  form a right angled triangle.

Answer 1

Given Vectors:

\(\vec a=3\hat i-2\hat j+\hat k\)

\(\vec b=\hat i-3\hat j+5\hat k\)

\(\vec c=2\hat i+\hat j-4\hat k\)

First show that the vectors form a triangle, so we use the addition of vector

Hence these vectors form a triangle

Now we will use Pythagoras theorem to prove this is a right angle triangle.

Therefore these vectors form a right angled triangle.