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  • Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 4 maths

Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 4 maths

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Answer: None of these

Hint: Find \vec{a}+\vec{b}+\vec{c}

Given: If  \vec{a}, \vec{b}, \vec{c}  are three non-vectors no two of which are collinear and vector \vec{a}+\vec{b} is collinear with \vec{c}, \vec{b}+\vec{c} is collinear with \vec{a}  then \vec{a}+\vec{b}+\vec{c}=?

Solution: Let a+b=x c                                           …………. (1)

                     b+c=y a                                           …………. (2)

                Then a+b+c=?

Multiply equation (2) by 2

        2(b+c)=(y a) 2                                                        ...............(3)

        2 b+2 c=2 a y

Subtract equation (3) by eq (1)

        \begin{aligned} &2 b+2 c-2 a y-a-b+x c \\\\ &b+(2+x) c+(-2 y-1) a=0 \end{aligned}

Comparing both sides

        \begin{aligned} &b=0 \\ &(2+x) c=0 \\ &2 c=-x c \\ &x=-2 \end{aligned}

        \begin{aligned} &(-2 y-1) a=0 \\ &-2 y a=1 \\ &y=\frac{1}{-2 a} \end{aligned}

 

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