Q. 135.0( 1 Vote )

Using vectors, fi

Answer :

Let the points be A (λ, –10, 3), B (1, –1, 3), C (3, 5, 3).

Let us define the position vectors of A, B and C.





Then,






And






And since, A, B and C are collinear.


Then, it has a relation as such


, where k is scalar quantity.




Comparing the coefficients of and . We get


1 – λ = k (3 – λ)


And 9 = 15k


First, we need to find the value of k.


So take 9 = 15k




Substitute the value of k in (1 – λ) = k (3 – λ)



5(1 – λ) = 3(3 – λ)


5 – 5λ = 9 – 3λ


5λ – 3λ = 5 – 9


2λ = –4



λ = –2


Hence, the value of λ is –2.


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