# Get Answers to all your Questions

#### Please solve RD Sharma class 12 chapter Determinants exercise 5.3 question 2 subquestion (ii) maths textbook solution

Answer: Yes, points are collinear.

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

$Given\! : \left ( 1,-1 \right ),\left ( 2,1 \right )\: and \: \left ( 4,5 \right )\! .$

$Explanation\! : V\! ertices\; are \left ( 1,-1 \right ),\left ( 2,1 \right )\: and \: \left ( 4,5 \right )\! .$

$Determinant\!= \begin{vmatrix} X_{1} &Y_{1} &1 \\ X_{2} &Y_{2} &1 \\ X_{3} &Y_{3} &1 \end{vmatrix}$

$= \begin{vmatrix} 1 &-1 &1 \\ 2 &1 &1 \\ 4 &5 &1 \end{vmatrix}$

$= 1\! \begin{vmatrix} 1 &1 \\ 5 &1 \end{vmatrix}-\left (-1 \right )\! \begin{vmatrix} 2 &1 \\ 4 &1 \end{vmatrix}+1\! \begin{vmatrix} 2 &1 \\ 4 &5 \end{vmatrix}$

$= 1\! \left (1-5 \right )+1\! \left ( 2-4 \right )+1\! \left ( 10-4 \right )$

$= 1\! \left ( -4 \right )+1\! \left ( -2 \right )+1\! \left ( 6 \right )$

$= -4-2+6$

$= -6+6$

$= 0$

Hence, points are collinear.