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Explain solution for RD Sharma maths class 12 chapter 22 Algebra of vectors exercise 22.8 question 10 maths textbook solution

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Answer: Vectors are coplanar

Hint: From vectors as a linear combination to prove they are coplanar

\RightarrowGiven \overrightarrow{a},\overrightarrow{b},\overrightarrow{c}  & \overrightarrow{d} be four position vectors.

If these vectors are coplanar then, l\overrightarrow{d}+m\overrightarrow{b}+n\overrightarrow{c}+w\overrightarrow{d}=0 where, l,m,n and w be some scalars

As per given condition

\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}  & \overrightarrow{d} are coplanar if they are in the form of

3\overrightarrow{a}-2\overrightarrow{b}+\overrightarrow{c}-2\overrightarrow{d}=0

Comparing,

l = 3

m = -2

n = 1

w = -2

Now, l+m+n+w=3-2+1-2=0

Thus, vectors are coplanar. Where l, m, n and w are non-zero scalar simultaneously.

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