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  • Explain solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 7 sub question 2 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 7 sub question 2 maths textbook solution

Answers (1)

Answer: vectors are not co-planar

Hint: The coefficients of a,b and c

\RightarrowGiven:  \begin{aligned} &\vec{a}+ \vec{b}+3 \vec{c}, \end{aligned} \begin{aligned} &2\vec{a}+ \vec{b}+3 \vec{c} \end{aligned} and \begin{aligned} &\vec{a}+ \vec{b}+ \vec{c} \end{aligned}

Solution : We know that

Three vectors are coplanar if any one of them can be expressed sa the linear combination of other two vectors.

Let

\begin{aligned} &\vec{a}+2 \vec{b}+3 \vec{c}=x(2 \vec{a}+\vec{b}+3 \vec{c})+y(\vec{a}+\vec{b}+\vec{c}) \\ &\vec{a}+2 \vec{b}+3 \vec{c}=\vec{a}(2 x+y)+\vec{b}(x+y)+\vec{c}(3 x+y) \end{aligned}

Comparing the coefficients of L.H.S and R.H.S.

2x+y=1                                                                  ....(1)

x+y=2                                                                      ....(2)

3x+y=3                                                                  ....(3)

Solving (1) and (2)

2x+y=1

\underline{x+y=2}

x            =-1

And from (i)

2\times \left ( -1 \right )+y=1

y=1+2

y=3

There is no value of x and y that can satisfy the equation (3)

Thus, vectors are not co-planar

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