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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 18 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 23 Scalar or Dot  Products  Exercise 23.1 Question 18 Maths Textbook Solution.

Answers (1)

Answer: proved

Hint: you must know the rules of solving vectors

Given: if either \vec{a}=\vec{0} or \vec{b}=\vec{0} then \vec{a}.\vec{b}=0 

But the inverse need not be true, justify with example

Solution: let us assume that either.

\mid \vec{a}\mid =0 or \mid \vec{b}\mid =0

Then, \vec{a}.\vec{b}=\mid \vec{a}\mid \mid \vec{b}\mid\cos \theta =0

Now let us assume that \vec{a}.\vec{b}=0

\Rightarrow \mid \vec{a}\mid \mid \vec{b}\mid\cos \theta =0

But here we cannot say that either\mid \vec{a}\mid =0 or \mid \vec{b}\mid =0

For example, Let,

\begin{aligned} &\vec{a}=2 \hat{\imath}+\hat{\jmath}+3 \hat{k} \text { and } \vec{b}=-3 \hat{\imath}+2 \hat{k} \\\\ &\text { Here, }|\vec{a}|=\sqrt{4+1+9}=\sqrt{14} \quad \neq 0 \\\\ &|\vec{b}|=\sqrt{9+0+4}=\sqrt{13} \quad \neq 0 \\\\ &\text { But }(\vec{a} \cdot \vec{b})=(2 \hat{\imath}+\hat{\jmath}+3 \hat{k}) \cdot(-3 \hat{\imath}+2 \hat{k}) \\\\ &=-6+0+6 \\\\ &\Rightarrow 0 \end{aligned}

 

 


 

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