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

Question

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

Answer 1

Given Data:

\(\vec a = 4\hat i-3\hat j+\hat k\) 

\(\vec b=2\hat i-4\hat j+5k\) 

\(\vec c=\hat i-\hat j\) 

= -2 × 3 + (-1) × (-2) + 1 × 4

= -6 + 2 + 4

Angle A right angle, ABC is right angle triangle.