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  • Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 7

Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 7

Answers (1)

Final Answer : (l, m, n)=\left(\frac{2}{3}, \frac{2}{3}, \frac{-1}{3}\right)

Hint:

(a,b,c) of a vector \left(a i^{{\wedge}}+b j^{\wedge}+c k^{\wedge}\right)  are direction ratio of that vector.

Given:

Vector?\left(2 i^{\wedge}+2 \hat{\jmath}-k^{\wedge}\right)

To Find: 

Direction cosine of vector.

Solution:

If  l,m,n  Direction cosine and a,b,c ane direction ratios, then

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

\therefore l=\frac{2}{\sqrt{2^{2}+2^{2}+(-1)^{2}}}, \quad m=\frac{2}{\sqrt{2^{2}+2^{2}+(-1)^{2}}}, \quad n=\frac{-1}{\sqrt{2^{2}+2^{2}+(-1)^{2}}}

\therefore l=\frac{2}{\sqrt{9}}, \quad m=\frac{2}{\sqrt{9}}, \quad n=\frac{-1}{\sqrt{9}}

Therefore  (l, m, n)=\left(\frac{2}{3}, \frac{2}{3},-\frac{1}{3}\right)

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