alleryVector $4\hat i + 13\hat j - 18\hat k$ expressed as a linear combination of $\hat i - 2\hat j + 3\hat k$ and $2\hat i + 3\hat j - 4\hat k$ has coefficients $(m, n)$:
A$(2, 3)$
B$(-2, 3)$
C$(3, -2)$
D$(-3, 2)$
Answer & Solution
Correct answer: B. $(-2, 3)$
Set $4\hat i + 13\hat j - 18\hat k = m(\hat i - 2\hat j + 3\hat k) + n(2\hat i + 3\hat j - 4\hat k)$.
**Equating components:** $m + 2n = 4$ and $-2m + 3n = 13$.
**Solving:** $m = -2, n = 3$.
Check the $\hat k$ component: $3(-2) - 4(3) = -18$ ✓.
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