Cauchy-Schwartz inequality, triangle inequality
Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.
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`.
Show that `|veca|vecb+|vecb|` is perpendicular to `|veca|vecb-|vecb|veca`, for any two nonzero vectors `veca and vecb`
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)`