alleryFind the value of $\lambda$ and $\mu$ if the non-zero, non-collinear vectors $\vec a$ and $\vec b$ satisfy $\vec a + 3\vec b = 2\lambda \vec a - \mu \vec b$:
A$\lambda = 1/2,\ \mu = -3$
B$\lambda = -1/2,\ \mu = 3$
C$\lambda = 2,\ \mu = -3$
D$\lambda = 1,\ \mu = -3$
Answer & Solution
Correct answer: A. $\lambda = 1/2,\ \mu = -3$
Non-collinear $\vec a, \vec b$ form a basis
⇒ coefficients on each side must match.
Coefficient of $\vec a$: $1 = 2\lambda$ ⇒ $\lambda = 1/2$.
Coefficient of $\vec b$: $3 = -\mu$ ⇒ $\mu = -3$.
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