The line passing through the points 5,1,a,3,b,1 crosses the yz-plane at the point 0,172,−132then

The line passing through the points $(5, 1, a), (3, b, 1)$ crosses the $y z -$ plane at the point $(0, \frac{17}{2}, \frac{- 13}{2})$ then

A
$a = 2, b = 8$
B
$a = 4, b = 6$
C
$a = 6, b = 4$
D
$a = 8, b = 2$

Solution:

The $y z -$ plane cuts the line segment joining the points $A (x_{1}, y_{1}, z_{1}), B (x_{2}, y_{2}, z_{2})$ in the ratio $- x_{1} : x_{2}$

Hence, the $y z -$ plane divides the line segment joining the points $(5, 1, a), (3, b, 1)$ in the ratio $5 : 3$ externally

Hence the point of division is $(0, \frac{5 b - 3}{2}, \frac{5 - 3 a}{2}) = (0, \frac{17}{2}, - \frac{13}{2})$

Equate the corresponding coordinates, we get $a = 6, b = 4$

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