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  • please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 1 maths textbook solution

please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 1 maths textbook solution

Answers (1)

best_answer

\sqrt{3}

Hint:

               Let |\vec {a}|=|\vec {b}|=1

Given:

If  \vec {a}and \vec {b} are two unit vectors such that \left |\vec {a+b} \right | is unit vector, thena-b\left |\vec {a} -\vec {b} \right |

Solution:

As \left |\vec {a+b} \right | is unit vector,  |\vec {a}|=|\vec {b}|=1

\begin{aligned} &|\vec{a}+\vec{b}|=1 \\ &|\vec{a}+\vec{b}|^{2}=1 \\ &|\vec{a}|^{2}+|\vec{b}|^{2}+2 a b=1 \\ \end{aligned}

\begin{aligned} &2+2(a \cdot b)=1 \\ &-2(a \cdot b)=1 \\ &|\vec{a}-\vec{b}|^{2}=|\vec{a}|^{2}+|\vec{b}|^{2}-2 a b \\ \end{aligned}

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

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