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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 17 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 17 Maths.

Answers (1)

Answer:

2 \hat{\imath}-4 \hat{\jmath}+4 \hat{k}

Hint:

Unit vector  =\frac{\vec{A}}{|\vec{A}|} , new vector = 6\times  unit vector of  2 \vec{a}-\vec{b}+3 \vec{c}

Given:

\vec{a}=(\hat{\imath}+\hat{\jmath}+\hat{k}), \vec{b}=(4 \hat{\imath}-2 \hat{\jmath}+3 \hat{k}), \vec{c}=(\hat{\imath}-2 \hat{\jmath}+\hat{k})

Solution:

\begin{aligned} &\text { Let } \vec{A}=2 \vec{a}-\vec{b}+3 \vec{c} \\\\ &=2 \hat{\imath}+2 \hat{\jmath}+2 \hat{k}-4 \hat{\imath}+2 \hat{\jmath}-3 \hat{k}+3 \hat{\imath}-6 \hat{\jmath}+3 \hat{k} \\\\ &=\hat{\imath}-2 \hat{\jmath}+2 \hat{k} \end{aligned}
 

\begin{aligned} &|2 \vec{a}-\vec{b}+3 \vec{c}|=\sqrt{1^{2}+2^{2}+2^{2}} \\\\ &=\sqrt{9}=3 \end{aligned}

 

Let \vec{B}  be the new vector

\begin{aligned} &\vec{B}=6 \hat{A}=6 \frac{\vec{A}}{|\vec{A}|} \\\\ &=6 \times \frac{\vec{A}}{3}=2 \vec{A} \\\\ &=2(\hat{\imath}-2 \hat{\jmath}+2 \hat{k}) \\\\ &=2 \hat{\imath}-4 \hat{\jmath}+4 \hat{k} \end{aligned}

 

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