UGC NET CSE | September 2013 | Part 3 | Question: 63

Question

The parametric representation of the line segment between the position vectors $P_1(2,3)$ and $P_2(5,4)$ is given as

• A. $x(t) = 2+ 7t, y(t)=0 \leq t \leq \infty \quad 3+7t$
• B. $x(t) = 2+ 10t, y(t)=0 \leq t \leq 1 \quad 3+7t$
• C. $x(t) = 2+ 3t, y(t)=0 \leq t \leq 1 \quad y(t)=3+t$
• D. $t(x,y)=14t \quad 0 \leq t \leq 1$

Answer 1

The parametric representation of a line) Given two points   (x₁, y₁)   and   (x₂, y₂),   the point   (x, y)   is on the line determined by   (x₁, y₁)   and   (x₂, y₂)   if and only if there is a real number t such that

x = (1 - t)x₁ + tx₂,

and                                                           y = (1 - t)y₁ + ty₂

_{here x1=2 ,x2= 5   y1=3,y2=4   putting these values} 

_{x=(1-t)2+t*5 =>x=3t+2}

_{y=(1-t)3+t*4=>y=t+3}     

_{hence ans is C}