If \(\rm \vec{i} - a\vec{j} + 5\vec{k}\)and \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) are parallel vectors then b 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:

\(\rm \vec{i} - a\vec{j} + 5\vec{k}\) and \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) are parallel vectors,

Therefore, \(\rm \vec{i} - a\vec{j} + 5\vec{k}= λ (\rm 3\vec{i} - 6\vec{j} + b\vec{k})\)

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

⇒ 1 = 3λ, ∴ λ = 1/3

⇒ -a = -6λ

⇒ 5 = bλ .... (1)

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

5 = b × (1/3)

So, b = 15