If the angle θ between the vectors a→ = 2 x2 i→ + 4 xj→ + k→ and b→ = 7 i→ - 2 j→ + xk→ is such that 900 < θ < 1800 then x lies in the interval

cosθ<0 ⇒ 14x2-8x+x<0 ⇒ 14x2-7x<0 7x(2x-1)<0 x∈(0, 12)

cosθ<0 ⇒ 14x2-8x+x<0 ⇒ 14x2-7x<0 7x(2x-1)<0 x∈(0, 12)

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If the angle $θ$ between the vectors $\vec{a} = 2 x^{2} \vec{i} + 4 x \vec{j} + \vec{k}$ and $\vec{b} = 7 \vec{i} - 2 \vec{j} + x \vec{k}$ is such that $90^{0} < θ < 180^{0}$ then x lies in the interval

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$(0, \frac{1}{2})$

$(1, \frac{3}{2})$

$(\frac{1}{2}, 1)$

$(\frac{1}{2}, \frac{3}{2})$

answer is A.

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$cosθ < 0 \Rightarrow 14 x^{2} - 8 x + x < 0 \Rightarrow 14 x^{2} - 7 x < 0 7 x (2 x - 1) < 0 x \in (0, \frac{1}{2})$ Question Image

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