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  • Provide Solution For R. D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 18 Maths Textbook Solution.

Provide Solution For R. D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 18 Maths Textbook Solution.

Answers (1)

Answer: 2

Hint: You must know the rules of vector functions

Given: If a vector makes angles with \alpha ,\beta &\gamma with OX, OY and OZ respectively, Write \sin ^{2}\alpha +\sin ^{2}\beta +\sin ^{2}\gamma

Solution: Suppose, a vector \vec{OP}makes angles \alpha ,\beta &\gamma  with OX, OY and OZ respectively

            Then direction cosines of vectors are given by l=\cos \alpha, m=\cos \beta, n=\cos \gamma

            Consider,

                        \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=\left(1-\cos ^{2} \alpha\right)+\left(1-\cos ^{2} \beta\right)+\left(1-\cos ^{2} \gamma\right)

                                                                       \begin{aligned} &=3-\left(\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma\right)\\ &=3-\left(l^{2}+m^{2}+n^{2}\right)\\ &=3-1 \quad\left[l^{2}+m^{2}+n^{2}=1\right]\\ &=2 \end{aligned}

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