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  • Explain solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22 point 8 question 7 sub question 1 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 7 sub question 1 maths textbook solution

Answers (1)

Answer: vectors are not co-planar

Hint: If vectors are in linear combination then they are coplanar and if they can’t be represented then they are not.

\RightarrowGiven the vectors as follows:

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

Comparing coefficient of \overrightarrow{a},\overrightarrow{b} & \overrightarrow{c}

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

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

-2x-3y= 3                                                  ...............(3)

Subtracting equation (1) and (2)

x+y=2

\underline{x+y=-1}

No solution can be obtained

Hence given vectors are non-coplanar

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