Show that points P(-2, 3, 5), Q(1, 2, 3) and R(7, 0, -1) are collinear.

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Parallel and Collinear Vectors, Direction Ratios of a Line | PadhAiPro

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TextParallel and Collinear VectorsDirection Ratios of a Line

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Direction ratios of a vector parallel to line (x–1)/2 = – y = (2z+1)/6 are :

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Find the equation of the line which bisects the line segment joining points A(2, 3, 4) and B(4, 5, 8) and is perpendicular to the lines (x–8)/3 = (y+19)/(–16) = (z–10)/7 and (x–15)/3 = (y–29)/8 = (z–5)/(–5).

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Direction Ratios of a Line

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Assertion (A) : A line through the points (4, 7, 8) and (2, 3, 4) is parallel to a line through the points (−1, −2, 1) and (1, 2, 5). Reason (R) : Lines r→ = a₁→ + λb₁→ and r→ = a₂→ + μb₂→ are parallel if b₁→ · b₂→ = 0.

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Two vectors a→ = a₁î + a₂ĵ + a₃k̂ and b→ = b₁î + b₂ĵ + b₃k̂ are collinear if

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