1.

If (1,λ), (3,−2)  and (−3,16) are collinear. Find the value of λ

Answer»

Let A(1,λ), B(3,-2), C(-3,16) be the vertices of abc, then the area of the triangle formed by them would be zero. 

⇒ 0 = \(\frac{ 1}{2}|(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))| \)

 0 = 1(-2-16) + 3(16 - λ) + -3(λ + 2)

 0 = -18 + 48 - 6 - 3λ - 3λ

∴ 6λ = 24 ∴ λ = 4



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