Points A( ) and B( ) are fixed

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Points A(

2,\,-3,\,1

) and B(

7,\,2,\,4

) are fixed. A point R lies on the line segment AB such that

\vec{AR} = t\,\vec{AB}

where

0 \le t \le 1

. (i) Express the position vector of R in terms of

t

. (ii) If the distance AR is 3 units, set up an equation in

t

and determine its possible value(s). (iii) For each value of

t

obtained, find the coordinates of R and the vector

\vec{BR}

\hat{i},\,\hat{j},\,\hat{k}

form.