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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 18 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 18 Maths.

Answers (1)

Answer:

\frac{15}{\sqrt{10}} \hat{\imath}+\frac{5}{\sqrt{10}} \hat{\jmath}

Hint:

A vector having magnitude 1 and parallel to  \vec{a}=1 \frac{\vec{a}}{|\vec{a}|}

Given:

\vec{a}=(2 \hat{\imath}+3 \hat{\jmath}-\hat{k}), \vec{b}=(\hat{\imath}-2 \hat{\jmath}+\hat{k})

Solution:

If  \vec{c}  is the resultant of  \vec{a} \text { and } \vec{b}

\begin{aligned} &\vec{c}=(2 \hat{\imath}+3 \hat{\jmath}-\hat{k})+(\hat{\imath}-2 \hat{\jmath}+\hat{k}) \\\\ &\vec{c}=3 \hat{\imath}+\hat{\jmath}+0 \hat{k} \end{aligned}

Now, a vector having magnitude 5 and parallel to \vec{c}

\begin{aligned} &\frac{5 \vec{c}}{|\vec{c}|}=\frac{5(3 \hat{\imath}+\hat{j})}{\sqrt{3^{2}+1^{2}}} \\\\ &=\frac{15}{\sqrt{10}} \hat{\imath}+\frac{5}{\sqrt{10}} \hat{\jmath} \end{aligned}

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