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 The point with position vectors 5î - 2ĵ,  8î - 3ĵ,  aî - 12ĵ are collinear if the value of a is 

  1. 31
  2. 51
  3. 42
  4. 35

Answer (Detailed Solution Below)

Option 4 : 35
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Detailed Solution

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Concept:

Three or more points are collinear, if slope of any two pairs of points is same.

The slope of a line passing through the distinct points (x1, y1) and (x2, y2) is 

Calculation:

Here, 

Let, A = (5, -2), B = (8, -3), C = (a, -12)

Now, slope of AB = Slope of BC = Slope of AC ....(∵ points are collinear)

 

⇒ a - 8= 27

⇒ a = 27 + 8 = 35

Hence, option (4) is correct.

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