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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 4 Sub Question 2 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 4 Sub Question 2 Maths Textbook Solution.

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Answer :- \left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ]=0

Hint :- vectors are coplanar if scalar triple product is zero.

Given:- \begin{aligned} &\vec{a}=\hat{\imath}-2 \hat{\jmath}+3 \hat{k} \\ \end{aligned}

\begin{aligned} &\vec{b}=-2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k} \\ &\vec{c}=\hat{\imath}-3 \hat{\jmath}+5 \hat{k} \end{aligned}

For vectors,\hat{a},\hat{b} &\hat{c}   if \left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ]=0.  vectors are coplanar. 

\begin{aligned} &\therefore\left[\begin{array}{lll} \vec{a} & \vec{b} & c \end{array}\right]=\left|\begin{array}{ccc} 1 & -2 & 3 \\ -2 & 3 & -4 \\ 1 & -3 & 5 \end{array}\right| \\ \end{aligned}

\begin{aligned} &=1(15-12)+2(-10+4)+3(6-3) \\ \end{aligned}

\begin{aligned} &= & 3-12+9 \\ \end{aligned}

\begin{aligned} &= & 0 \end{aligned}

Thus, vectors are coplanar

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