Maths-
General
Easy
Question
The points with position vectors 
and 
are collinear for
- Only integrals values of λ
- no value of λ
- all real values of λ
- Only rational values of λ
Hint:
We are given position vectors of three points. We have to find the value of λ such that the vectors are parallel to each other. Vectors are parallel to each other when they are scalar multiple of each other.
The correct answer is: all real values of λ
Let the position vectors of the three vectors be denoted as follows:
Now the vector from point S to point T will be
The vector from point T to point U will be
For the points to be collinear, the vectors should be collinear too. Two vectors are collinear if they are scalar multiple of each other. Let the scalar multiple be p.
So, λ will have all real values.
The points are collinear for all real values of λ.
For such questions, we should know how to find the vector joining two points. Also, we should know the condition for two vectors to be collinear.
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