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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 10

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 10

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Answer:- x+y+z=2

Hint:-To solve this equation, we use substitute method

Given:- If the vector \vec{a}=2 \hat{i}-(y+z) \hat{j}+5 \hat{k} \text { and } \vec{b}=(x+y) \hat{i}+3 \hat{j}+(z+x) \hat{k} are then x+y+z=____

Solution:- \vec{a}=\vec{b}

2 \hat{i}-(y+z) \hat{j}+5 \hat{k}=(x+y) \hat{i}+3 \hat{j}+(z+x) \hat{k}

Comparing we get

\begin{array}{ll} x+y=2 & \text {...( } i) \\\\ -(y+z)=3 & \text {...(ii) } \\\\ , z+x=5 & \text {...(iii) } \end{array}

From eq (ii) we make y the subject to the equation

Substitute for y=-3-z  in the equation(i)

\begin{aligned} &x-3-z=2 \quad ......(iv)\\ \\ &x-z=5 \end{aligned}

Solving eq(iii) & (iv)

\begin{aligned} &z+x+x-z=5+5 \\\\ &2 x=10 \\\\ &x=5 \end{aligned}

Put the values of x in eq(iii)

\begin{aligned} &z+5=5 \\\\ &z=0 \end{aligned}

 Put the values of z in eq(ii)

\begin{aligned} &\mathrm{y}=-3 \\\\ &\text { so, } \mathrm{x}+\mathrm{y}+\mathrm{z}=5+(-3)+0 \\\\ &\quad=5-3 \\\\ &\quad=2 \end{aligned}

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