vectors

If I prove the dot product of two vectors is zero, is it then assumed that the vectors are perpendicular or is an extra line of work required to prove why it means theyre perpendicular?

We are doing all of 4 unit integration for the exam but only up to dot product and that level for 3d vectors. Could someone please send some up to date papers as thsc is all old syllabus. Thanks!

Mainly ones with pulleys, tension, incline planes and stuff like that. Most questions I find are really easy using normal force vectors.

What Cambridge Lessons is this dot point referring to: ME-V1.2 Operations with Vectors - solve problems involving displacement, force and velocity involving vector concepts in two dimensions. If anyone has a question bank for the dot point, please send it through lol.

Im talking about this formula: I was doing a hunters hill high extension 2 trial and they asked to find the min value of |z|. Would I need to derive this formula or can i just use it in an exam?

Hi all, I don't really have a specific example question from a paper (will look for one), but this is the type of thing that I really can't seem to do - is anyone able to explain this? I.e., how to use projections properly to find the shortest perpendicular distance between two vectors? Thanks!

The question basically is: Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k). I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.

hey!!! I was wondering if anyone knew how to solve part B for this question. I can't seem to wrap my head around it. The answer is x= -3. Thank you!!

I need help with part a.

Hello everyone! Can anybody help me to solve these question? (sorry I'm very bad at Maths, took me forever but I still couldn't figure out o_O) 1. (HSC 1982): A biased coin is found to have probability 0.7 of showing a head when tossed. b) What is the most likely combination of heads and tails...