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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

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

Answers (1)

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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