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