Q1: If a = i + 2j - k and b = j + k, find a unit vector perpendicular to both a and b.
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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!
What sides touch?
OP touches PQ
PQ touches QR
QR touches OR
OP touches OR.
If it's a square, then the angles should be right angles. Evaluating any of the dot products of touching sides should give 0 if this is the case.
Then show that the lengths are equal, and you've got a square.
See how you go from there.