Let \(\vec a=2\hat i-\hat j+\hat k\)
\(\vec b=3\hat i-4\hat j-4\hat k\)
\(\vec c=\hat i-3\hat j-5\hat k\)
\(\vec a.\vec b=(2\hat i-\hat j+\hat k).(3\hat i-4\hat j-4\hat k)\)
= 6 + 4 - 4
= 6 \(\neq0\)
\(\vec b.\vec c=(3\hat i-4\hat j-4\hat k).(\hat i-3\hat j-5\hat k)\)
= 3 + 12 + 20
= 35 \(\neq\) 0
\(\vec a.\vec c=(2\hat i-\hat j-\hat k).(\hat i-3\hat j-5\hat k)\)
= 2 + 3 - 5
= 0
\(\therefore\) Angle between \(\vec a\) & \(\vec c\) is 90°.
\(\therefore\) \(\vec a,\vec b\)& \(\vec c\)will form a right triangle.