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Let $$P(1, –2), Q(–2, 1), R(3, 5)$$ be three points in the cartesian plane.

(a) Calculate the vectors $PQ$ and $PR$.

(b) Draw a diagram indicating the points $P, Q$ and $R$ and the vectors and.

(c) Calculate the angle between the vectors $PQ$ and $PR$.

  1. Let $P, Q $ be points with co-ordinates $P(2, 3), Q(-2, 4)$.

(a) Determine any value(s) of $k$ for which the vector $V=(K,3)$ is parallel to $PQ$.

(b) State the condition used to determine if two vectors are perpendicular.

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1 Answer

up vote 3 down vote accepted

Vector PQ = (-2-1, 1-(-2)) = (-3, 3). Now you can find PR...

Drawing the diagram is easy I think...

To solve question 2)(a), what is the definition of a colinear vector?

To solve question 2)(b), write the scalar product $<,>$. For example $<u,v>=u_1v_1+u_2v_2$ where $u=(u_1,u_2)$ and $v=(v_1,v_2)$.

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Yes you're right, I'm sorry for that. Didn't have enough reputation to comment yesterday... I've edited it, can you remove your down vote @Avatar ? –  mak Sep 26 '12 at 7:49
    
it's okay now. (+1) :) –  Aang Sep 26 '12 at 9:23
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