Q31 of 36 Page 10

Find the value of λ, if four points with position vectors and are coplanar.[CBSE 2017]

We have-





Now,





To prove that points A, B, C, D are coplanar, we have to show that




⇒ (-2)[(-1)(3-λ)-(2)(-4)] - (-4)[(-1)(3-λ)-(2)(-3)]


+ (-6)[(-1)(-4)-(-1)(-3)]


= 0


⇒ (-2)[λ-3+8] - (-4)[λ-3+6] + (-6)[4-3] = 0


⇒ (-2)(λ+5) + 4(λ+3) -6 = 0


⇒ -2λ-10+4λ+12-6 = 0


⇒ 2λ = 4


∴ λ = 2


Thus, the value of λ is 2 for which points A, B, C, D are coplanar.

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