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  • Please solve RD Sharma class 12 chapter Determinants exercise 5.3 question 10 maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise 5.3 question 10 maths textbook solution

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Answer: x=3

Hints: Use vertices in the determinant formula and equate it with zero because if points are collinear then determinant will be zero and then find the value of x.

Given: (x, -2), (5,2) and (8,8) are collinear.

Explanation: Vertices are (x, -2), (5,2) and (8,8)

\text { Determinant }=\left|\begin{array}{lll} X_{1} & Y_{1} & 1 \\ X_{2} & Y_{2} & 1 \\ X_{3} & Y_{3} & 1 \end{array}\right|=0

                            \Rightarrow \left|\begin{array}{lll} x & -2 & 1 \\ 5 & 2 & 1 \\ 8 & 8 & 1 \end{array}\right|=0

                            \Rightarrow x\left|\begin{array}{ll} 2 & 1 \\ 8 & 1 \end{array}\right|-(-2)\left|\begin{array}{cc} 5 & 1 \\ 8 & 1 \end{array}\right|+1\left|\begin{array}{cc} 5 & 2 \\ 8 & 8 \end{array}\right|=0

                            \Rightarrow x(2-8)+2(5-8)+1(40-16)=0

                            \Rightarrow x(-6)+2(-3)+1(24)=0

                            \Rightarrow -6x-6+24=0

                           \Rightarrow -6x+18=0

                           \Rightarrow 6x=18

                          \Rightarrow x=3

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Gurleen Kaur

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