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  • Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 8 maths

Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 8 maths

Answers (1)

Hint:

\text {Volume of parallelopiped} = \left [ \overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \right ]

Where,

\overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \text { are adjacent edges }

Given:

Adjacent edges

\begin{aligned} &\overrightarrow{a}+\overrightarrow{b}, \overrightarrow{b}+\overrightarrow{c},\overrightarrow{c}+\overrightarrow{a} \text { and }\\ &\overrightarrow{a}=2\widehat{i}-3\widehat{j}+5\widehat{k}\\ &\overrightarrow{b}=3\widehat{i}-4\widehat{j}+5\widehat{k}\\ &\overrightarrow{c}=5\widehat{i}-3\widehat{j}-2\widehat{k}\\ &\therefore \overrightarrow{a}+\overrightarrow{b}=(2+3)\overrightarrow{i}+(-3-4)\overrightarrow{j}+(5+5)\overrightarrow{k}\\ &=5\overrightarrow{i}-7\overrightarrow{j}+10\overrightarrow{k} \end{aligned}

\begin{aligned} &\overrightarrow{b}+\overrightarrow{c}=(3+5)\widehat{i}+(-4-3)\widehat{j}+(5-2)\widehat{k}\\ &=8\widehat{i}-7\widehat{j}+3\widehat{k}\\ &\overrightarrow{c}+\overrightarrow{a}=(5+2)\widehat{i}+(-3-3)\widehat{j}+(-2+5)\widehat{k}\\ &=7\widehat{i}-6\widehat{j}+3\widehat{k} \end{aligned}

\begin{aligned} &\therefore \end{aligned} Volume of parallelopiped=

\begin{aligned} &\begin{vmatrix} 5 &-7 &10 \\ 8 &-7 &3 \\ 7 &-6 &3 \end{vmatrix}\\ &=5(-21+18)+7(24-21)+10(-48+49)\\ &=-15+21+10\\ &=16 \end{aligned}

Note : Given all option are incorrect

Posted by

Gurleen Kaur

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