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  • please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22.5 question 3 maths textbook solution

please solve RD sharma class 12 chapter 22 Algebra of vector exercise 22.5 question 3 maths textbook solution

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2\sqrt{3}\hat{i}+2\hat{j}

Hint: a units vectors parallel to \vec{a}=\hat{a}=\frac{\vec{a}}{\left | \vec{a} \right |}

Given: \vec{a}=\sqrt3\hat{i}+\hat{j}

Solution:

               As we know \hat{i} and \hat{j} are vector in x an y direction

               Let \vec{a}=\sqrt3\hat{i}+\hat{j}

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

               Here x=\sqrt3 and y=1

                \left |\vec{a} \right |=\sqrt{(\sqrt3)^{2}+1^{2}}\\ \left |\vec{a} \right |=\sqrt{4}\\ \left |\vec{a} \right |=2

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

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

Required vector =4a\Rightarrow \hat{a}=4 \times \frac{1}{2}\left ( \sqrt{3}\hat{i}+\hat{j} \right )

\Rightarrow 2\left ( \sqrt{3}\hat{i}+\hat{j} \right )\\ \Rightarrow 2\sqrt{3}\hat{i}+2\hat{j}

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