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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 31 Sub Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products  Exercise 23.1 Question 31 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer:  \mid \vec{a}\mid =\frac{8\sqrt{8}}{\sqrt{63}},    \mid \vec{b}\mid =\sqrt{\frac{8}{63}}

Hint:  You must know the rules of solving vectors.

Given: \left ( \vec{a}+\vec{b} \right ).\left ( \vec{a}-\vec{b} \right )=8 and \mid \vec{a}\mid =8\mid \vec{b}\mid

Solution:  Given that,

\begin{aligned} &(\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})=8 \text { and }|\vec{a}|=8|\vec{b}| \\\\ &|\vec{a}|^{2}-|\vec{b}|^{2}=8 \\\\ &(8|\vec{b}|)^{2}-|\vec{b}|^{2}=8 \end{aligned}

\begin{aligned} &64|\vec{b}|^{2}-|\vec{b}|^{2}=8 \\\\ &63|\vec{b}|^{2}=8 \\\\ &|\vec{b}|^{2}=\frac{8}{63} \\ \end{aligned}

\begin{aligned} &|\vec{b}|=\sqrt{\frac{8}{63}} \\\\ &\therefore|\vec{a}|=\frac{8 \sqrt{8}}{\sqrt{63}} \text { and }|\vec{b}|=\sqrt{\frac{8}{63}} \end{aligned}

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