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

Question

Question

Answer 1

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 \(\rm \frac{y_2 -y_1 }{x_2-x_1}\)

Calculation:

Here, \(\rm 5\hat i-2\hat j, 8\hat i-3\hat j, a\hat i-12\hat j \)

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

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

\(\rm \frac{-3-(-2)}{8-5}=\frac{-12-(-3)}{a-8}\\ ⇒ \frac{-1}{3}=\frac{-9}{a-8}\)

⇒ a - 8= 27

⇒ a = 27 + 8 = 35

Hence, option (4) is correct.