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  • Need solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 31

Need solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 31

Answers (1)

Answer:

11 \sqrt{5} \text { square units }

Hint:

To solve this we use    \vec{c}=\frac{\vec{a}+\vec{b}}{|\vec{a}+\vec{b}|}

Given:

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

Solution:      

\begin{aligned} &\vec{c}=\vec{a}+\vec{b}=3 \hat{i}-6 \hat{j}+2 \hat{k} \\\\ &\vec{c}=\frac{\vec{a}+\vec{b}}{|\vec{a}+\vec{b}|} \\\\ &=\frac{3}{7} \hat{i}-\frac{6}{7} \hat{j}+\frac{2}{7} \hat{k} \end{aligned}

\begin{aligned} &A=|\vec{a} \times \vec{b}|=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 2 & -4 & 5 \\ 1 & -2 & -3 \end{array}\right| \\\\ &=|22 \hat{i}+11 \hat{j}+0 \hat{k}| \\\\ &=11|2 \hat{i}+\hat{j}| \end{aligned}

\begin{aligned} &=11 \sqrt{(2)^{2}+(1)^{2}} \\\\ &=11 \sqrt{5} \end{aligned}                            

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