Question:medium
If the angle between the vectors $\vec{a}=x\hat{i}+3\hat{j}+\hat{k}$ and $\vec{b}=x\hat{i}-x\hat{j}+2\hat{k}$ is acute, then $x$ lies is
If the angle between the vectors $\vec{a}=x\hat{i}+3\hat{j}+\hat{k}$ and $\vec{b}=x\hat{i}-x\hat{j}+2\hat{k}$ is acute, then $x$ lies is
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Logic Tip: The "Wavy Curve Method" is perfect here. Mark roots 1 and 2 on a number line. Start with a '+' sign on the rightmost interval $(2, \infty)$, alternate to '-' for $(1, 2)$, and back to '+' for $(-\infty, 1)$. We want the regions $>0$ (the '+' regions).
Updated On: Apr 27, 2026
- $(-\infty,-1)\cup(1,\infty)$
- $(-\infty,-1)\cup(2,\infty)$
- $(-\infty,1)\cup(2,\infty)$
- $(-\infty,0)\cup(1,\infty)$
- $(-\infty,0)\cup(2,\infty)$
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The Correct Option is C
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