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  • Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 16.

Provide solution for RD Sharma Maths Class 12 Chapter 24 Vector or Cross Product exercise Very Short Answer Question, question 16.

Answers (1)

ANSWER:           

\frac{\hat{i}-\hat{\jmath}+\hat{k}}{\sqrt{3}}

HINT:

Just find the cross product of vectors.

GIVEN:

Given, two vectors,      \left ( \widehat{i}+\widehat{j} \right ) and \left ( \widehat{j}+\widehat{k} \right )                                         

SOLUTION:

\begin{aligned} &\text { Let } \vec{a}=\hat{\imath}+\hat{\jmath}+0 \hat{k} \\ &\qquad \vec{b}=0 \hat{\imath}+\hat{\jmath}-\hat{k} \\ &\text { Now } \vec{a} \times \vec{b}=\left|\begin{array}{lll} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right| \\ &\quad=\hat{\imath}(1-0)-\hat{\jmath}(1-0)+\hat{k}(1-0) \\ &\quad=-\hat{\imath}-\hat{\jmath}+\hat{k} \end{aligned}

Now unit vector perpendicular to \overrightarrow{a}\times \overrightarrow{b} is \widehat{n}

\begin{aligned} \therefore \hat{n} &=\frac{(\vec{a} \times \vec{b})}{|\vec{a} \times \vec{b}|} \\ &=\frac{\hat{\imath}-\hat{\jmath}+\hat{k}}{\sqrt{(1)^{2}+(-1)^{2}+(1)^{2}}} \\ &=\frac{\hat{i}-\hat{\jmath}+\hat{k}}{\sqrt{3}} \end{aligned}

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