সরলরেখার সমীকরণ
(1,1), (cosα, sinα) ও (secα, cosecα) সমরেখ হলে, α=কত?
30°
45°
60°
90°
⇒y2−y1x2−x1=y3−y1x3−x1⇒sinα−1cosα−1=cosecα−1secα−1⇒sinα−1cosα−1=cosα(1−sinα)sinα(1−cosα)⇒(sinα−1cosα−1)∗cosα(sinα−1)sinα(cosα−1)=0⇒(sinα−1)(cosα−1)(1∗cotα)=0 \begin{array}{l} \Rightarrow \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{3}-y_{1}}{x_{3}-x_{1}} \\ \Rightarrow \frac{\sin \alpha-1}{\cos \alpha-1}=\frac{\operatorname{cosec} \alpha-1}{\sec \alpha-1} \\ \Rightarrow \frac{\sin \alpha-1}{\cos \alpha-1}=\frac{\cos \alpha(1-\sin \alpha)}{\sin \alpha(1-\cos \alpha)} \Rightarrow\left(\frac{\sin \alpha-1}{\cos \alpha-1}\right) * \frac{\cos \alpha(\sin \alpha-1)}{\sin \alpha(\cos \alpha-1)}=0 \\ \Rightarrow \frac{(\sin \alpha-1)}{(\cos \alpha-1)}(1 * \cot \alpha)=0 \end{array} ⇒x2−x1y2−y1=x3−x1y3−y1⇒cosα−1sinα−1=secα−1cosecα−1⇒cosα−1sinα−1=sinα(1−cosα)cosα(1−sinα)⇒(cosα−1sinα−1)∗sinα(cosα−1)cosα(sinα−1)=0⇒(cosα−1)(sinα−1)(1∗cotα)=0
Now, 1−cotα=0 1-\cot \alpha=0 1−cotα=0
cotα=1 \cot \alpha=1 cotα=1
∴α=45∘ \therefore \alpha=45^{\circ} ∴α=45∘
দৃশ্যকল্প ১: x−2y+1=0 x-2 y+1=0 x−2y+1=0
দৃশ্যকল্প ২ : P⃗=i^−2j^+k^;Q⃗=2i^+j^−3k^ \vec{P}=\hat{i}-2 \hat{j}+\hat{k} ; \vec{Q}=2 \hat{i}+\hat{j}-3 \hat{k} P=i^−2j^+k^;Q=2i^+j^−3k^
AB রেখার সমীকরণ x+y=4;C,AB x+y=4 ; C, A B x+y=4;C,AB এর মধ্যবিন্দু।
(2,3), (6,9), (-2,1) শীর্ষবিশিষ্ট বৃত্তের পরিকেন্দ্রের স্থানাঙ্ক নিচের কোনটি?
