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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 10 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot Products  Exercise 23.1 Question 10 Maths Textbook Solution.

Answers (1)

Answer: proved

Hint: you must know the rules of proving vector

Given: if \vec{a},\vec{b},\vec{c} are these mutually perpendicular unit vectors, prove that \mid \vec{a}+\vec{b}+\vec{c}\mid =\sqrt{3}

Solution: given that \vec{a},\vec{b}and \vec{c} are unit vectors

So, \mid \vec{a}\mid =1,\mid \vec{b}\mid =1,\mid \vec{c}\mid =1

Since they are mutually perpendicular

\begin{aligned} &\vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}=\vec{c} \cdot \vec{a}=0 \\ \end{aligned}

Now,\begin{aligned} &|\vec{a}+\vec{b}+\vec{c}|^{2}=|\hat{a}|^{2}+|\hat{b}|^{2}+|\hat{c}|^{2}+2 \hat{a} \cdot \hat{b}+2 \hat{b} \cdot \hat{c}+2 \hat{c} \cdot \hat{a} \\ \end{aligned}

\begin{aligned} &=1+1+1+0+0+0 \\\\ &|\vec{a}+\vec{b}+\vec{c}|^{2} \Rightarrow 3 \\\\ &|\vec{a}+\vec{b}+\vec{c}| \Rightarrow \sqrt{3} \end{aligned}

=Proved

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