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  • Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.6 Question 2 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.6 Question 2 Maths Textbook Solution.

Answers (1)

Answer:

The unit vector will be  \frac{3}{13} \hat{\imath}+\frac{4}{13} \hat{\jmath}-\frac{12}{13} \hat{k}

Hint:

Use vector magnitude formula.

Given:

3 \hat{\imath}+4 \hat{\jmath}-12 \hat{k}

Solution:

Let the unit vector in the direction of  \vec{A}=3 \hat{\imath}+4 \hat{\jmath}-12 \hat{k} \text { be } \vec{B}

So, any unit vector in the direction of   \vec{A}=3 \hat{\imath}+4 \hat{j}-12 \hat{k}   will be

 \vec{B}=\frac{\vec{A}}{|\vec{A}|}

So, the magnitude of the vector

|\vec{A}|=\sqrt{3^{2}+4^{2}+(-12)^{2}}
\begin{aligned} &|\vec{A}|=\sqrt{9+16+144}=\sqrt{169} \\ &|\vec{A}|=13 \end{aligned}

So, the unit vector

 \vec{B}=\frac{3 \hat{\dagger}+4 \hat{\jmath}-12 \hat{k}}{13}=\frac{3}{13} \hat{i}+\frac{4}{13} \hat{\jmath}-\frac{12}{13} \hat{k}

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