If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].

Question

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ ABC, [ ∠ ABC is the angle between the vectors ].

Philoid · Accepted Answer

Given points are A (1, 2, 3), B (-1, 0, 0) and C (0, 1, 2)

∠ABC is the angle between vectors

We know

⇒ ∠ABC = cos^-1(10/√102)