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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 6 sub question 2 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 6 sub question 2 maths textbook solution

Answers (1)

Answer: vectors are not co-planar

Hint: Form vectors in linear combination of other two vectors

\RightarrowGiven, three vectors

Let,

\begin{aligned} &A=\hat{i}+2 \hat{j}+3 \hat{k} \\ &B=2 \hat{i}+\hat{j}+3 \hat{k} \\ &C=\hat{i}+\hat{j}+\hat{k} \\ &A=x B+y C \\ &\hat{i}+2 \hat{j}+3 \hat{k}=x(2 \hat{i}+\hat{j}+3 \hat{k})+y(\hat{i}+\hat{j}+\hat{k}) \\ &\hat{i}+2 \hat{j}+3 \hat{k}=\hat{i}(2 x+y)+\hat{j}(x+y)+\hat{k}(3 x+y) \end{aligned}

Comparing coefficient of \hat{i},\hat{j} & \hat{k}

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

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

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

 Subtracting (1) and (2)

\begin{aligned} &2 x+y=1\\ &\begin{aligned} &x+y=2 \\ &x=-1 \end{aligned}\\ &x+y=2\\ &-1+y=2\\ &y=3\\ &\text { Put } x=-1 \quad \& \quad y=3 \quad \text { in }\\ &3 x+y=3\\ &\text { Substitute } x=-1 \text { and } y=3 in \left ( 3 \right ) \end{aligned}

3x+y=3

Substitute x=-1 and y=3

3\left ( -1 \right )+3=3

= -3+3

=0

\neq 3  

Thus, as x and y do not satisfy the third equation

Hence, given vectors are non-coplanar

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