If \(\vec a = 2\hat{\imath} + m\hat{\jmath} - n\hat{k}\) and \(\vec b = l\hat{\imath} - 3\hat{\jmath} + 4\hat{k}\) such that \(\vec a = 2\vec b\) then the value of \(14l + m + n\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
Two vectors are equal only when their corresponding components are equal.
\(2\vec b = 2l\hat{\imath} - 6\hat{\jmath} + 8\hat{k}\)
Comparing with \(\vec a = 2\hat{\imath} + m\hat{\jmath} - n\hat{k}\):
\(2l = 2\), so \(l = 1\)
\(m = -6\)
\(-n = 8\), so \(n = -8\)
\(14l + m + n = 14 - 6 - 8 = 0\)