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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 31 Sub Question 3 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products  Exercise 23.1 Question 31 Sub Question 3 Maths Textbook Solution.

Answers (1)

Answer:  \mid \vec{a}\mid =2,\mid \vec{b}\mid =1

Hint:  You must know the rules of solving vectors.

Given: \left ( \vec{a}+\vec{b} \right ).\left ( \vec{a}-\vec{b} \right )=3 and \mid \vec{a}\mid =2\mid \vec{b}\mid   and

Solution:  Given that,

\begin{aligned} &(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=3 \text { and }|\vec{a}|=2|\vec{b}| \\\\ &|\vec{a}|^{2}-|\vec{b}|^{2}=3 \\\\ &(2|\vec{b}|)^{2}-|\vec{b}|^{2}=3 \end{aligned}

\begin{aligned} &4|\vec{b}|^{2}-|\vec{b}|^{2}=3 \\\\ &3|\vec{b}|^{2}=3 \\\\ &|\vec{b}|^{2}=1 \\ \end{aligned}

\begin{aligned} &|\vec{b}|=1 \\\\ &|\vec{a}|=2|\vec{b}| \\\\ &|\vec{a}|=2(1) \\\\ &|\vec{a}|=2 \\\\ &\therefore|\vec{a}|=2 \text { and }|\vec{b}|=1 \end{aligned}

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