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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 19 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 19 Maths.

Answers (1)

Answer:

2\sqrt{2}   units

Hint:

By triangle law of addition.

Given:

\begin{aligned} &A \vec{B}=\hat{\jmath}+\hat{\imath} \\\\ &A \vec{C}=3 \hat{\imath}-\hat{\jmath}+4 \hat{k} \end{aligned}

Solution:             

                                                         

\begin{aligned} B \vec{C}=A \vec{C}-A \vec{B} &=(3 \hat{\imath}-\hat{\jmath}+4 \hat{k})-(\hat{\jmath}+\hat{\imath}) \\ &=2 \hat{\imath}-2 \hat{\jmath}+4 \hat{k} \end{aligned}   [ By triangle law of addition ]

B \vec{D}=\frac{1}{2} B \vec{C}    ..as D is the midpoint of

  \begin{aligned} &=\hat{\imath}-\hat{\jmath}+2 \hat{k} \\ A \vec{D} &=A \vec{B}+B \vec{D} \end{aligned}  [ By triangle law of addition ]

\begin{aligned} &=(\hat{\imath}+\hat{\jmath})+(\hat{\imath}-\hat{\jmath}+2 \hat{k}) \\ &=2 \hat{\imath}+2 \hat{k} \\ |A \vec{D}| &=\sqrt{2^{2}+2^{2}}=\sqrt8 \\ &=2 \sqrt{2} \text { units } \end{aligned}

     

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