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  • please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 5 maths textbook solution

please solve RD sharma class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 5 maths textbook solution

Answers (1)

\sqrt{2}

Hint:

               a is perpendicular to b

Given:

If a and  b are mutually perpendicular unit vector, then \left |\vec{a}+\vec{b} \right |

Solution:

               \left |\vec{a} \right |=\left |\vec{b} \right |=1 , \vec{a} .\vec{b} =0…as they are perpendicular                              … (i)

Now,   

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

\begin{aligned} &=1+1+2(0)=2 &&&&&& [Use (i)]\\ \end{aligned}

\begin{aligned} &|\vec{a}+\vec{b}|=\sqrt{2} &&&&&& \left[\because \sqrt{1^{2}+1^{2}}=\sqrt{2}\right] \end{aligned}

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