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  • Explain Solution R.D. Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 49 Maths Textbook Solution.

Explain Solution R.D. Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 49 Maths Textbook Solution.

Answers (1)

Answer: Proved

Hints: You must know the rules of solving vectors.

Given: If \vec{a}\vec{b} are two vector such that, \mid \vec{a}+\vec{b}\mid=\mid \vec{b}\mid, prove \vec{a}+2\vec{b} is to \vec{a}

Solution:  Given that,

\mid \vec{a}+\vec{b}\mid=\mid \vec{b}\mid

Squaring both sides,

\begin{aligned} &\Rightarrow|\vec{a}+\vec{b}|^{2}=|\vec{b}|^{2} \\ &\Rightarrow|\vec{a}|^{2}+|\vec{b}|^{2}+2 \vec{a} \cdot \vec{b}=|\vec{b}|^{2} \\ &\Rightarrow|\vec{a}|^{2}+2 \vec{a} \cdot \vec{b}=0 \end{aligned}

Now,

\begin{aligned} &\Rightarrow(\vec{a}+2 \vec{b}) \cdot \vec{a} \\ &\Rightarrow \vec{a} \cdot \vec{a}+2 \vec{b} \vec{a} \\ &\Rightarrow|\vec{a}|^{2}+2 \vec{a} \cdot \vec{b} \quad \therefore[\vec{b} \cdot \vec{a}=\vec{a} \cdot \vec{b}] \end{aligned}

\Rightarrow 0

So, \vec{a}+2\vec{b} is perpendicular to \vec{a}.

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