Question

(i) If \(\bar a\) = 3i – j – 5k and \(\bar b\) = i – 5j + 3k Show that \(\bar a\) + \(\bar b\) and a bare perpendicular.

(ii) Given the position vectors of three points as A(i – j + k); B(4i + 5j + 7k) C(3i + 3j + 5k)

(a) Find \(\bar {AB}\) and \(\bar {BC}\)

(b) Prove that A,B and C are collinear points.

Answer 1

(i) \(\bar a+\bar b\) = 4i - 6j - 2k, \(\bar a - \bar b\) = 2i + 4j - 8k