Particles P and Q move in a plane with constant velocities. At time t = 0 the position vectors of P and Q, relative to a fixed point O in the plane, are (16i - 12j) m and -5i + 4j) m respectively. The velocity of P is (i + 2j) m/s and the velocity of Q

is (2i + j) m/s. Find the shortest distance between P and Q in the subsequent motion. This is an m4 question from the edexcel June 2015 paper. First I would explain to the student that I would form an equation equating the distance to the position vector of Q subtracted from the postion vector of P. Then I would tell the student that the next step is to find the square of the absolute distance by squaring the coefficient of the i and j vectors and adding them. After this the equation should be differentiated with respect to t.The differential will be equal to 0, as it is a minimum. This will be used to solve t and then the value of t will be substituted into the initial distance equation and then Pythagoras's theorem will be used to find the distance.

Answered by Further Mathematics tutor

2289 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4metres. Calculate the maximum speed of the particle.


a) Find the general solution to the differential equation: f(x)=y''-12y'-13y=8. b) Given that when x=0, y=0 and y'=1, find the particular solution to f(x).


Find the reflection of point P(2,4,-6) in the plane x-2y+z=6


The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning