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  • Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 10

Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 10

Answers (1)

Answer         : not equal

Hint               : To solve this w use determinant method

Given             :

                        \begin{aligned} &\vec{a}=2 \hat{\imath}+5 \hat{\jmath}-7 \hat{k} \\ &\vec{b}=3 \hat{i}+4 \hat{\jmath}+\hat{k} \\ &\vec{c}=\hat{\imath}-2 \hat{\jmath}-3 \hat{k} \end{aligned}

Solution       : \vec{a} \times \vec{b}=\left|\begin{array}{ccc} \hat{\imath} & \hat{j} & \hat{k} \\ 2 & 5 & -7 \\ -3 & 4 & 1 \end{array}\right|

\begin{aligned} &\vec{a}=33 \hat{\imath}+19 \hat{\jmath}+23 \hat{k} \\\\ &\vec{b} \times \vec{c}=\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ -3 & 4 & 1 \\ 1 & -2 & -3 \end{array}\right| \\\\ &\vec{l}=-10 \hat{\imath}-8 \hat{\jmath}+2 \hat{k} \end{aligned}

\begin{aligned} &\vec{d} \times \vec{c}=\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 33 & 19 & 23 \\ 1 & -2 & -3 \end{array}\right| \\\\ &(\vec{a} \times \vec{b}) \times \vec{c}=-11 \hat{\imath}+122 \hat{\jmath}-85 \hat{k} \\\\ &\vec{a} \times \vec{l}=\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & 5 & -7 \\ -10 & -8 & 2 \end{array}\right| \end{aligned}

\begin{aligned} &\vec{a} \times(\vec{b} \times \vec{c})=-46 \hat{\imath}+66 \hat{\jmath}+34 \hat{k} \\\\ &(\vec{a} \times \vec{b}) \times \vec{c} \neq \vec{a}(\vec{b} \times \vec{c}) \end{aligned}

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