Q1: If a = i + 2j - k and b = j + k, find a unit vector perpendicular to both a and b.
Q2: The points P and Q have position vectors a + b and 3a - 2b respectively when referred from the origin O. Given that OPQR is a parallelogram, express the vectors PQ and PR in terms of a and b. [I have found PQ = 2a - 3b; PR = a - 4b] By evaluating 2 scalar products, show that if OPQR is a square, then|a| = 2|b| .
Thank you for helping!