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  • Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 11

Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 11

Answers (1)

Answer: x=5

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: (3,-2), (x,2) and (8,8).

Explanation: Vertices are (3,-2), (x,2) and (8,8).

\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} 3 & -2 & 1 \\ x & 2 & 1 \\ 8 & 8 & 1 \end{array}\right|=0

\Rightarrow 3\left|\begin{array}{ll} 2 & 1 \\ 8 & 1 \end{array}\right|-(-2)\left|\begin{array}{cc} x & 1 \\ 8 & 1 \end{array}\right|+1\left|\begin{array}{cc} x & 2 \\ 8 & 8 \end{array}\right|=0

\Rightarrow 3(2-8)+2(x-8)+1(8x-16)=0

\Rightarrow 3(-6)+2(x-8)+8x-16=0

\Rightarrow -18+2x-16+8x-16=0

\Rightarrow 10x-50=0

\Rightarrow x=\frac{50}{10}

\Rightarrow x=5

Posted by

Gurleen Kaur

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