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  • Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 26

Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 26

Answers (1)

Answer:

3 \sqrt{5} square units

Hint:

 To solve this we use area of triangle formula

Given:

\begin{aligned} &\overrightarrow{O A}=\hat{i}+2 \hat{j}+3 \hat{k} \\\\ &\overrightarrow{O B}=-3 \hat{i}-2 \hat{j}+\hat{k} \end{aligned}

Solution:

\begin{aligned} &A=\frac{1}{2}|\overrightarrow{O A} \times \overrightarrow{O B}| \\\\ &=\frac{1}{2}\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 2 & 3 \\ -3 & -2 & 1 \end{array}\right| \end{aligned}

\begin{aligned} &=\frac{1}{2}|8 \hat{i}-10 \hat{j}+4 \hat{k}| \\\\ &=\frac{1}{2} \sqrt{64+100+16} \end{aligned}

=\frac{\sqrt{180}}{2}=\sqrt{45}\\\\

=3 \sqrt{5}  square units

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