If \(\rm x\vec{i} - 2\vec{j} + 3\vec{k}\) and \(\rm 2\vec{i} - 4\vec{j} + y\vec{k}\) are parallel vectors then x is equal to?

Question

Question

Answer 1

Concept:

If \({\rm{\vec a\;and\;\vec b}}\) are two vectors parallel to each other then \({\rm\vec{a} = λ \vec{b}}\) or \(\rm \vec{a} × \vec{b} =0\)

Calculation:

Given:

\(\rm x\vec{i} - 2\vec{j} + 3\vec{k}\) and \(\rm 2\vec{i} - 4\vec{j} + y\vec{k}\) are parallel vectors,

Therefore, \(\rm x\vec{i} - 2\vec{j} + 3\vec{k} = λ (\rm 2\vec{i} - 4\vec{j} + y\vec{k})\)

Equating the coefficient of \(\rm \vec{i},\vec{i} \;and\; \vec{k}\)

⇒ x = 2λ .... (1)

⇒ -2 = -4λ

∴ λ = 1/2

Put the value of λ in equation (1), we get

x = 2 × (1/2)

So, x = 1