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ABCD is a parallelogram with A as the or...

ABCD is a parallelogram with A as the origin. vec b` and `vec d` are the position vectors of B and D respectively.

a.What is the position vector of C?
(b) What is the angle between `vec(AB)` and `vec (AD)`?
(c) Find `vec(AC)`
(d) If `|vec(AC)| = |vec (BD)|`, show that ABCD is rectangle.

Text Solution

Verified by Experts

The correct Answer is:
(b) `cos theta = (vec b. Vec d)/(|vec b||vec d|)`
(c) `vec(AC) = vec(AB) + vec (BC) = vec (AB) + vec (AD) = vec b + vec d`
(d) `vec (AB) bot vec(BC)`.
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