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  • Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 10

Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 10

Answers (1)

Final Answer:  6 i^{\wedge}-9j^{\wedge}+18 k^{\wedge}

Hint:

Use direction ratio to find direction cosine.

Given:

|\vec{r}|=21 \text { and }(a, b, c)=(2,-3,6)

To Find: 

vector \vec{r}

Solution:

Direction cosine is related to Direction ratio as

l=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}, m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}, n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}

l=\frac{2}{\sqrt{2^{2}+(-3)^{2}+6^{2}}}, m=\frac{-3}{\sqrt{2^{2}+(-3)^{2}+6^{2}}}, n=\frac{6}{\sqrt{2^{2}+(-3)^{2}+6^{2}}}

\begin{aligned} &l=\frac{2}{7}, m=\frac{-3}{7}, n=\frac{6}{7} \\\\ \end{aligned}

\vec{r}=|\vec{r}|\left(l i^{\wedge}+m_{j}^{\wedge}+n k^{\wedge}\right)

\begin{aligned} &\text { Now } \vec{r}=21\left(\frac{2}{7} i^{\wedge}+\frac{(-3)}{7} \hat{\jmath}+\frac{6 k^{\wedge}}{7}\right) \\\\ &\vec{r}=3\left(2 i^{\wedge}-3 \hat{\jmath}+6 k^{\wedge}\right) \\\\ &\vec{r}=6 i^{\wedge}-9 \hat{\jmath}+18 k^{\wedge} \end{aligned}

Therefore, the vector \vec{r} \text { is }\left(6 i^{\wedge}-9 j^{\wedge}+18 k^{\wedge}\right)

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