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$If the point P (\frac{3 a}{2}, 1) lies between the two different lines x + y = a and x + y = 2 a, then the least positive integral$ $value of a is$

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Solution

$Point (\frac{3}{2} a, 1) lies between two different lines x + y = a and x + y = 2 a . I f a p o i n t P (x_{1}, y_{1}) l i e s i n b e t w e e n t w o p a r a l l e l l i n e s L_{1} = 0 a n d L_{2} = 0 i f a n d o n l y i f L_{11} \times L_{22} < 0$
$\begin{array}{l} ∴ (\frac{3}{2} a + 1 - a) (\frac{3}{2} a + 1 - 2 a) < 0 \\ (\frac{a}{2} + 1) (1 - \frac{a}{2}) < 0 \\ (a + 2) (a - 2) > 0 \\ a \in (- \infty, - 2) \cup (2, \infty) \end{array}$
$T h e r e f o r e, t h e l e a s t p o s i t i v e i n t e g r a l v a l u e o f a i s 3$

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Pair of straight lines

Remember concepts with our Masterclasses.

If the point P3a2,1 lies between the two different lines x+y=a and x+y=2a , then the least positive integral value of a is

Point 32a,1 lies between two different lines x+y=a and x+y=2a . If a point P(x1,y1) lies in between two parallel lines L1=0 and L2=0 if and only if L11×L22<0∴ 32a+1−a32a+1−2a<0a2+11-a2<0a+2a-2>0a∈(−∞,−2)∪(2,∞)Therefore, the least positive integral value of a is 3

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$If the point P (\frac{3 a}{2}, 1) lies between the two different lines x + y = a and x + y = 2 a, then the least positive integral$ $value of a is$