Cauchy-Schwartz inequality, triangle inequality
- Product of Two Vectors - Projection of a Vector on a Line
Show that `|veca|vecb+|vecb|` is perpendicular to `|veca|vecb-|vecb|veca`, for any two nonzero vectors `veca and vecb`
If `veca = 2hati + 2hatj + 3hatk , vecb = -veci + 2hatj + hatk and vecc = 3hati + hatj` are such that `veca + lambdavecb` is perpendicular to `vecc`, then find the value of λ.
Find the angle between two vectors `veca` and `vecb` with magnitudes `sqrt3` and 2, respectively having `veca.vecb = sqrt6`.
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 `bar(BA)` and `bar(BC)`