OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीA vector \( \mathbf{A} = 8\hat{i} + 15\hat{j} \) is expressed as a linear combination \( \mathbf{A} = \lambda \mathbf{a} + \mu \mathbf{b} \), where \( \mathbf{a} = 2\hat{i} \) and \( \mathbf{b} = 3\hat{j} \). The values of real constants \( \lambda \) and \( \mu \) are respectively:
Correct answer · Option 1
\( \lambda = 4, \mu = 5 \)
Explanation
\( \mathbf{A} = 2\lambda\hat{i} + 3\mu\hat{j} = 8\hat{i} + 15\hat{j} \). Equating components gives \( 2\lambda = 8 \Rightarrow \lambda = 4 \) and \( 3\mu = 15 \Rightarrow \mu = 5 \).
