Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question

1 Answer 1

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 $v=(v_1,v_2)$.

share|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.