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  • Need Solution for R D Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 4 Sub Question 3 Maths Textbook Solution.

Need Solution for R D  Sharma Maths Class 12 Chapter 25 Scalar Triple Product  Exercise 25.1 Question 4 Sub Question 3  Maths Textbook Solution.

Answers (1)

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

=1\left ( 15-22 \right )+2\left ( -10+4 \right )+3\left ( 6-3 \right )

=3-12+9

=0

Thus, vectors are coplanar

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