# Math Help - Finding a vector

1. ## Finding a vector

P is the point 2,3
Q is the point 6,6

Write down vector PQ in column form. I got 4 over 3 (not sure how to use latex with this one)

The question:

PQRS is a prallelogram
Vector PR (not sure how to make the vector sign in latex) = 4 over 7
Find vector QS

I did -4 over -4 + 0 over 4 and got -4 over 1 as an answer.

Correct?

2. Anyone?

3. Hi

Your answer is correct but I haven't understood how you got it

$\vec{PR} = \binom{4}{7}$

$\vec{PQ} = \binom{4}{3}$

$\vec{QS} = \vec{QP} + \vec{PR} + \vec{RS} = 2 \vec{QP} + \vec{RS} = \binom{2 \times (-4) + 4}{2 \times (-3) + 7} = \binom{-4}{1}$

4. $\vec{QR}=\vec{PS}$
$\vec{PQ}=\vec{SR}=\binom{4}{3}$

Because $\vec{PR}=\binom{4}{7}$
$\vec{QR}=\binom{0}{4}=\vec{PS}$

Because $\vec{QS}=\vec{-PQ}+\vec{PS}$
$\vec{QS}=\binom{-4}{-3}+\binom{0}{4}=\binom{-4}{1}$

5. Well done

6. thanks