Let be two given vectors where vectors are non-collinear. The value of λ for which vectors are collinear is:

Question

Question

This question was previously asked in

JEE Mains Previous Paper 1 (Held On: 10 Jan 2019 Shift 2)

Answer 1

From question, the vectors are non-collinear.

Then, we can write,

for some non-zero scalar λ.

From question,

So, we can write,

for some k ∈ R -{0}

On substituting the values,

From question, as are non-collinear, therefore they are linearly independent.

⇒ (λ - 2) - k(4λ - 2) = 0 and (1 - 3k) = 0

Now,

⇒ 1 = 3k

On substituting value of ‘k’ in another obtained equation,

⇒ 3λ - 6 = 4λ - 2

∴ λ = -4