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  • Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors Exercise 22.9 Question 1 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 22 Algbra of Vectors Exercise 22.9 Question 1 Maths Textbook Solution.

Answers (1)

Answer: Yes

Given: Can a vector have direction angles 45^{o},60^{o},120^{o}

Hint: Verify using l^{2}+m^{2}+n^{2}=1

Explanation: Given angles are 45^{o},60^{o},120^{o}

Now the cosines of the direction angles are \cos 45^{o},\cos 60^{o},\cos 120^{o}

i.e.  \frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{-1}{2}\left[\because \cos 45^{\circ}=\frac{1}{\sqrt{2}}, \cos 60^{\circ}=\frac{1}{2}, \cos 120^{\circ}=-\frac{1}{2}\right]

We know if l ,m ,n be the direction cosines of any line then l^{2}+m^{2}+n^{2}=1

\therefore L.H.S= l^{2}+m^{2}+n^{2}

\begin{aligned} &=\left(\frac{1}{\sqrt{2}}\right)^{2}+\left(\frac{1}{2}\right)^{2}+\left(-\frac{1}{2}\right)^{2} \\ &=\frac{1}{2}+\frac{1}{4}+\frac{1}{4} \\ &=1 \end{aligned}

=R.H.S

Hence \frac{1}{\sqrt{2}},\frac{1}{2},\frac{-1}{2} are the direction cosines of the vector having direction angles \cos 45^{o},\cos 60^{o},\cos 120^{o}

So, the given angles can be the direction angles of a vector.

 

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