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  • Need solution for RD sharma maths class 12 chapter 22 Algebra of Vector exercise 22.5 question 10

Need solution for RD sharma maths class 12 chapter 22 Algebra of Vector exercise 22.5 question 10

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Answer: \frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}

Hint: a unit vector parallel to

 \vec{a}=\hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |}\\ \left | \vec{a} \right |=\sqrt{x^{2}+y^{2}}

Given: \vec{a}=\hat{i}+\sqrt{3}\hat{j}

Solution:

We can find the magnitude of \vec{a}

\left | \vec{a} \right |=\sqrt{x^{2}+y^{2}}

Here x = 1 and  y=\sqrt{3}

\left |\vec{a} \right |=1^{2}+(\sqrt{3})^{2}\\ =\sqrt{1+3}=4\\ \left |\vec{a} \right |=2

Unit vector parallel to \vec{a}=\hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |}\\

=\frac{1}{2}\left ( \hat{i}+\sqrt{3}\hat{j} \right )\\ =\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}

 

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