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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 4 Sub Question 1 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise 25.1 Question 4 Sub Question 1 Maths textbook Solution.

Answers (1)

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

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

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

\begin{aligned} &\vec{b}=3 \hat{i}+2 \hat{\jmath}+7 \hat{k} \\ &\vec{c}=5 \hat{\imath}+6 \hat{\jmath}+5 \hat{k} \end{aligned}

 

For any three vectors,   if their scalar triple product is zero. i.e. \left [ \vec{a}\: \: \vec{b}\: \: \vec{c}\right ]=0 than they are coplanar.

 

\begin{aligned} &\therefore\left[\begin{array}{lll} \vec{a} & \vec{b} & c \end{array}\right]=\left|\begin{array}{ccc} 1 & 2 & -1 \\ 3 & 2 & 7 \\ 5 & 6 & 5 \end{array}\right| \\ \end{aligned}

\begin{aligned} &=1(10-42)-2(15-35)-1(18-10) \\ \end{aligned}

\begin{aligned} &= & -32+40-8 \\ \end{aligned}

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

Thus, vectors are coplanar

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