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The vectors $2 i - m j + 3 m k$ and $(1 + m) i - 2 m j + k$ include an acute angle for

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m<–2 or m>–1/2

m>2, m<1/2

all values of m

m > –2, m< –1/2

answer is C.

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Detailed Solution

$a . b > 0 \Rightarrow 2 + 2 m + 2 m^{2} + 3 m > 0 \Rightarrow 2 m^{2} + 5 m + 2 > 0 \Rightarrow (2 m + 1) (m + 2) > 0 \Rightarrow$

$\Rightarrow m \in (- \infty, - 2) \cup (- \frac{1}{2}, \infty)$

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