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  • Need solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 2 sub question (ii)

Need solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 2 sub question (ii)

Answers (1)

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Answer     :\sqrt{6}

Hint          : To solve this equation we use determinate formula then magnitude formula

Given       : \vec{a}=2 \hat{\imath}+\hat{k}

                    \begin{aligned} &\vec{b}=\hat{\imath}+\hat{\jmath}+\hat{k} \\ &\text { find }|\vec{a} \times \vec{b}| \end{aligned}

Solution  :

\begin{aligned} : \vec{a} \times \vec{b} &=\left|\begin{array}{lll} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & 0 & 1 \\ 1 & 1 & 1 \end{array}\right| \\\\ &=\hat{\imath}(0 \times 1-1 \times 1)-\hat{\jmath}(2 \times 1-1 \times 1)+\hat{k}(2 \times 1-0 \times 1) \\\\ &=-\hat{\imath}-\hat{\jmath}+2 \hat{k} \end{aligned}

\begin{aligned} |\vec{a} \times \vec{b}| &=\sqrt{1^{2}+1^{2}+2^{2}} \\\\ &=\sqrt{1+1+4} \\\\ &=\sqrt{6} \end{aligned}

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