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  • Explain Solution R.D. Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 12 Sub Question 2 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 12 Sub Question 2 Maths Textbook Solution.

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Answer:-  no value of c_{1}  can make \vec{a},\vec{b},\vec{c} coplanar

Hint :- If three vectors are coplanar than scalar triple product is zero.

Given:-\vec{a}=\hat{i}+\hat{j}+\hat{k}

\vec{b}=\hat{i}

\begin{aligned} &\vec{c}=c_{1} \hat{\imath}+c_{2} \hat{\jmath}+c_{3} \hat{k} \\ \end{aligned}

Also,\begin{aligned} &c_{2}=-1, c_{3}=1 \\ \end{aligned}

\begin{aligned} &\therefore \vec{c}=c_{1} \vec{l}-\vec{J}+\vec{k} \end{aligned}

For  \vec{a},\vec{b},\vec{c} to be co-planar  \left [ \vec{a},\vec{b},\vec{c} \right ]=0

\left[\begin{array}{lll} \vec{a} & \vec{b} & \vec{c} \end{array}\right]=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 0 & 0 \\ c_{1} & -1 & 1 \end{array}\right|

=1\left ( 0-0 \right )-1\left ( 1-0 \right )+1\left ( -1-0 \right )

=0-1-1

=-2

But =-2\neq 0

And no value of c_{1} will be enough to change the criteria. Thus no value of c_{1} can make\vec{a},\vec{b},\vec{c} coplanar. 

 

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