For the vectors , and , if , then the value of m + n is:

Question

Question

This question was previously asked in

NIMCET 2014 Official Paper

Answer 1

Concept:

If two vectors and are equal, then a₁ = b₁, a₂ = b₂ and c₁ = c₂.

Calculation:

We have .

⇒ 2î + 3ĵ = m(-4î + 2ĵ) + n(2î + ĵ)

⇒ 2î + 3ĵ = (-4m + 2n)î + (2m + n)ĵ

Equating the scalar coefficients, we get:

-4m + 2n = 2 ... (1)

2m + n = 3 ... (2)

Multiplying equation (2) by 2 and adding to equation (1), we get:

4n = 8

⇒ n = 2

Using either of the equations above, we also get:

m =

∴ m + n = 2 + = .