Posted in vectors.

What makes a mathematician a mathematician? Scientific studies say one thing above anything else: laziness1 We will go to extraordinary lengths to avoid doing any proper work. For example, I had a situation: I had two points - call them $P$ and $Q$ - and a line with the equation

Read More →
Posted in vectors.

Dear Uncle Colin, Apparently, the volume of a tetrahedron with three edges given by the vectors $\vec{AB}$, $\vec{AC}$ and $\vec{AD}$, is $\frac{1}{6} \left| \vec{AB} \cdot \br{\vec{AC}\times\vec{AD}} \right|$. Where does that come from? - Very Obviously Lacklustre Understanding of My Exam Hi, VOLUME, and thanks for your message! I think there

Read More →I recently listened to @mrhonner's episode of @myfavethm, in which he cited Varignon's Theorem as his favourite. What's Varignon's Theorem when it's at home? It states that, if you draw any quadrilateral, then connect the midpoints of adjacent sides, you get a parallelogram. Don't believe it? Try Mark's nifty geometry

Read More →
Posted in ask uncle colin, vectors.

Dear Uncle Colin Do you have any tips for sketching three-dimensional vectors? Every time we have an A-level question, my teacher says "draw a diagram!" but I don't know how to draw in 3D. - Got A Useless Sketching Situation Hi, GAUSS, and thank you for your message! Three-dimensional vectors

Read More →
Posted in ask uncle colin, vectors.

Dear Uncle Colin, I'm struggling a bit with my C4 vectors. Most of it is fine, except when I have to find a point $P$ on a given line such that $\vec{AP}$ is perpendicular to the line, for some known $A$. How do I figure that out? -- Any Vector

Read More →
Posted in ask uncle colin, vectors.

Dear Uncle Colin, I've got three points: $A$, with a position vector of $(2\bi + 4\bj)$, $B$, with a position vector of $(6\bi + 8\bj)$ and $C$, with a position vector of $(k\bi + 25\bj)$, and they all lie on the same straight line. I have to find $k$, and

Read More →
Posted in ask uncle colin, STEP, vectors.

Dear Uncle Colin, I'm struggling with this STEP question. The first two parts are fine -- equality holds when there is some constant $k$ for which $a = kx$, $b = ky$ and $c=kz$, and part (i) follows directly from the original inequality. I can get an answer to part

Read More →At granny's house, it always seems to go the same way after lunch: Bill and his cousin chase each other around the dining room, while the adults try to make head or tail of their toys. This Sunday was no different: the toy in question comprised a large number of

Read More →Need help with problem-solving? Fill out the short blue form on the left and get free tips on how to approach maths questions - delivered direct to your inbox twice a week → If you ever study GCSE vectors questions, you'll spot a pattern: there's normally a (relatively) straightforward first

Read More →If you ever study GCSE vectors questions, you'll spot a pattern: there's normally a (relatively) straightforward first part which involves writing down a few vectors, and then something like "show that points $O$, $X$ and $Y$ lie on a straight line." Pretty much every student I've ever worked with on

Read More →