# VECTORS mathematics

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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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 $v=(v_1,v_2)$.