Exercise 6.2
Question 7
यदि बिन्दुएँ (a,b),(a1,b1) तथा (a-a1 , b-b1) संरेख हैं तो दिखाएँ कि
[If the points (a,b),(a1,b1) and (a-a1 , b-b1)] are collinear , show that .]
$\frac{a}{a_{1}}=\frac{b}{b_{1}}$\
Sol :
∵(a,b),(a1,b1) तथा (a-a1 , b-b1) संरेख हैं
$\frac{1}{2}\left|\begin{array}{lll}a & b & 1 \\ a_{1} & b_{1} & 1 \\ a-a_1 & b-b_{1} & 1\end{array}\right|=0$
R1→R1-R2-R3
$\left|\begin{array}{ccc}0 & 0 & -1 \\ a_{1} & b_{1} & 1 \\ a_-a{_{1}} & b-b_{1} & 1\end{array}\right|=0$
R1 के सापेक्ष विस्तार करने पर ,
$-\left|\begin{array}{cc}a_{1} & b_{1} \\ a-a_{1} & b-b_{1}\end{array}\right|=0$
a1(b-b1)-b1(a-a1)=0
a1b-a1b1-b1a+a1b1=0
-b1a=-a1b
$\frac{a}{a_{1}}=\frac{b}{b_{1}}$
Question 8
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