Q1: Ifa=i+ 2j-kandb=j+k, find a unit vector perpendicular to bothaandb.

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Q2: The points P and Q have position vectorsa+band 3a- 2brespectively when referred from the origin O. Given thatOPQRis a parallelogram, express the vectors PQ and PR in terms ofaandb. [I have found PQ = 2a- 3b; PR =a- 4b] By evaluating 2 scalar products, show that ifOPQRis a square, then|a|$\displaystyle ^2 $= 2|b|$\displaystyle ^2 $.

Thank you for helping!