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  • Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 18.

Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 18.

Answers (1)

ANSWER:

y^2+ z^2

HINT:

Simplify using cross product.

GIVEN: \hat{r} =x \hat{i}+y \hat{j}+z \hat{k}

SOLUTION:

\begin{aligned} \hat{r} &=x \hat{i}+y \hat{j}+z \hat{k} \\ \therefore \hat{r} \times \hat{i} &=\left|\begin{array}{lll} \hat{i} & \hat{j} & \hat{k} \\ x & y & z \\ 1 & 0 & 0 \end{array}\right| \\ &=\hat{i}(0-0)-\hat{j}(0-z)+\hat{k}(0-y) \\ &=+z \hat{j}-y \widehat{k} \end{aligned}\begin{gathered} \therefore|\hat{r} \times \hat{i}|=\sqrt{(z)^{2}+(-y)^{2}} \\ |\hat{\imath} \times \hat{i}|=\sqrt{z^{2}+y^{2}} \end{gathered}

Squaring both the sides

\begin{aligned} |\hat{r} \times \hat{i}|^{2}=&\left(\sqrt{z^{2}+y^{2}}\right)^{2} \\ &|\hat{r} \times \hat{i}|=z^{2}+y^{2} \end{aligned}

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