Question

The vector equation of the line joining the points i - 2j + k and - 2j + 3k is [MP PET2003]
A)$ r = t(i + j + k)$
B) $r = {t_1}(i - 2j + k) + {t_2}(3k - 2j)$
C) $r = (i - 2j + k) + t(2k - i)$
D) $r = t(2k - i)$

Answer 1

Hint: in this question we have to find vector equation of line joining two given point. In order to find vector equation of line we must know the position vector of a point through which line passing and a vector parallel to line.



Formula Used:Equation of required line is given by
a + tb = 0
Where
a is a position vector of fixed point through which line is passing
b is a vector parallel to line
t is any constant



Complete step by step solution:Position vector of fixed point through which line is passing is a = i - 2j + k and another point c = - 2j + 3k
Vector which is parallel to the required line is given by
b=c-a
b = ( - 2j + 3k) - (i - 2j + k)
b = 2k - i
Put a and b in equation a + tb = 0
Required equation is
(i - 2j + k) + t(2k - i) = 0



Option ‘C’ is correct

Note: Here we need to remember that line which is joining two points a, c is parallel to (c-a). Straight line is a set of infinites points in which all points are linear.