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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 3 Sub Question 1 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise 25.1 Question 3 Sub Question 1 Maths textbook Solution.

Answers (1)

Answer :- 37 cubic units

Hint :- Use formula that volume of parallelepiped is \left [ \vec{a}\: \vec{b}\: \vec{c} \right ]

Given:\begin{aligned} &-\vec{a}=2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k} \\ \end{aligned}

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

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

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

                    \begin{aligned} &\quad=2(3)-3(5)+4(-7) \\ \end{aligned}

                    \begin{aligned} &=6-15-28 \\\ &=-37 \end{aligned}

∴Volume of parallelepiped,=\left [ \vec{a}\: \vec{b}\: \vec{c} \right ]

                                           =\mid -37\mid

                                            =37 \: Cubic \: Units

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