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The points with position vectors vecx + ...

The points with position vectors `vecx + vecy, vecx-vecy and vecx +λ vecy` are collinear for all real values of λ.

Text Solution

Verified by Experts

The correct Answer is:
True
Let position vectors of points A, B and C be
`vecx + vecy, vecx - vecy and vecx +λvecy`, respectively.
Then `vec(AB) = (vecx - vecy ) - (vecx + vecy) = -2 vecy`
Similarly, `vec(BC) = (vecx + λ vecy) - (vecx - vecy) = (λ+1)vecy`
Clearly `vec(AB) "||" vec(BC) AA λ in R`
Hence, A, B and C are collinear `AA λ inR`
Therefore, the statement is true.
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