TS EAMCET · Maths · Vector Algebra

Observe the following statements A. Three vectors are coplanar if one of them is expressible as a linear combination of the other two. R. Any three coplanar vectors are linearly dependent. Then, which of the following is true?

A Both \(A\) and \(R\) are true and \(R\) is the correct explanation of \(A\)
B Both \(A\) and \(R\) are true but \(R\) is not the correct explanation of \(A\)
C \(A\) is true, but \(R\) is false
D \(A\) is false, but \(R\) is true

Verified Solution

Answer & Solution

Correct Answer

(B) Both \(A\) and \(R\) are true but \(R\) is not the correct explanation of \(A\)

Step-by-step Solution

Detailed explanation

Both Statement A and \(\mathrm{R}\) are true. But \(\mathrm{R}\) is not correct explanation of A.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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