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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 9 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 23 Scalar or Dot Products  Exercise 23.1 Question 9 Maths Textbook Solution.

Answers (1)

Answer: Proved

Hint: you must know rule of proving vector properties

Given: if the sum of two unit vectors is a unit vector prove that magnitude of their difference is \sqrt{3}

Solution: Let their unit vectors are a, b, c. given, sum of unit vectors is a unit vector

\begin{aligned} &\therefore a+b=c \\\\ &|\hat{c}|^{2}=|\hat{a}+\hat{b}|^{2} \\\\ &|\hat{c}|^{2}=|a|^{2}+|b|^{2}+2|a||b| \cos \theta \\\\ &=1=1+1+2 \cos \theta \end{aligned}                                                        [\therefore|a|-|b|=|c|=1 \text { (unit vector) }]

\cos \theta =\frac{-1}{2}

Now\begin{aligned} &|\hat{a}-\hat{b}|^{2}=|a|^{2}+|b|^{2}-2|a||b| \cos \theta \\ \end{aligned}

\begin{aligned} &|\hat{a}-\hat{b}|^{2}=[1+1+1] \\ &|\hat{a}-\hat{b}|^{2}=[3] \\ &|a-b|=\sqrt{3} \end{aligned}

 

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