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  • Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 40 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 40 Maths Textbook Solution.

Answers (1)

Answer: Proved

Hints: You must know the rules of solving vectors.

Given:  If \vec{c}  is perpendicular to both \vec{a} and \vec{b} then prove that it is perpendicular to both \vec{a}+\vec{b}  and  \vec{a}-\vec{b}

Solution:  Given that \vec{c} is perpendicular to both \vec{a} and \vec{b}

\Rightarrow \vec{c}.\vec{a}=0 and \Rightarrow \vec{c}.\vec{b}=0

Now,

\begin{aligned} &\Rightarrow \vec{c}(\vec{a}+\vec{b})=\vec{c} \cdot \vec{a}+\vec{c} \cdot \vec{b} \\\\ &\Rightarrow 0+0=0 \end{aligned}

So, \vec{c} is perpendicular to \vec{a}+\vec{b}

Again,

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

So, \vec{c} is perpendicular to \vec{a}-\vec{b}

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