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  • Explain Solution R.D. Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 12 Sub Question 1 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 12 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer:c_{3}=2

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

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

\vec{b}=\hat{i}

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

If c 1 = 1 & c2 = 2 then find c3 which makes \vec{a} , \vec{b} & \vec{c}  are coplanar.

\begin{aligned} &\therefore \vec{c}=1 \vec{\imath}+2 \vec{\jmath}+\mathrm{c}_{3} \vec{k} \\ \end{aligned}

If \vec{a},\vec{b},\vec{c}  are coplanar than \left [ \vec{a}\: \vec{b}\: \vec{c} \right ]=0

\begin{aligned} &\therefore\left[\begin{array}{lll} \vec{a} & \vec{b} & \vec{c} \end{array}\right]=\left|\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 2 & c_{3} \end{array}\right|=0 \\ &1(0-0)-1\left(c_{3}-0\right)+1(2-0)=0 \\ &-c_{3}+2=0 \\ &\therefore-c_{3}+2=0 \\ &c_{3}=2 \end{aligned}

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